Area bounded by the lines y = |x| - 2 and y = 1 - |x - 1| is equal to:
- 4 sq. units
- 6 sq. units
- 2 sq. units
- 8 sq. units
Question types
APPLICATION OF INTEGRALS question types
378 questions across 7 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
378
Questions
7
Question groups
5
Question types
01
M.C.Q (1 Marks)
175 Q→02Assertion (A) & Reason (B) MCQ
4 Q→031 Marks
3 Q→042 Marks
1 Q→053 Marks
6 Q→064 Marks
179 Q→07Case study (4 Marks)
10 Q→Sample Questions
APPLICATION OF INTEGRALS questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
View full solution →
A rea bounded by the circle x2 + y2 = 1 and the curve | x | + | y | = 1 is:
View full solution →- $2\pi$
- $\pi-2$
- $\pi$
- $\pi+3$
The area of the region bounded by the curves y =| x – 2 |, x = 1, x = 3 and the x-axis is:
- 4
- 2
- 3
- 1
Area bounded by the curve $\text{y}=\log\text{x}$ and the coordinate axes is:
View full solution →- $2$
- $1$
- $5$
- $2\sqrt{2}$
The area of the region bounded by the curve x = 2y + 3 and the lines y = 1 and y = -1 is:
View full solution →- 4 sq. units
- $\frac{3}{2}\text{sq.}\text{ units}$
- 6 sq. units
- 8 sq. units
Directions: In these questions, a statement of Assertion is followed by a statement of Reason is given.Choose the correct answer out of the following choices:
Assertion: The area of the smaller region bounded by the ellipse $\frac{\text{x}^2}{9}+\frac{\text{y}^2}{4}=1$ the line $\frac{\text{x}}{3}+\frac{\text{y}}{2}=1$ is $\frac{3}{2}(\pi-2)\text{ sq.units}$
Reason: Formula to calculate the area of the smaller region bounded by the ellipse $\frac{\text{x}^2}{\text{a}^2}+\frac{\text{y}^2}{\text{b}^2}=1$ and the line $\frac{\text{x}}{\text{a}}+\frac{\text{y}}{\text{b}}=1$ is $\frac{\text{ab}}{4}(\pi-2) \text{ sq.units}$
View full solution →Assertion: The area of the smaller region bounded by the ellipse $\frac{\text{x}^2}{9}+\frac{\text{y}^2}{4}=1$ the line $\frac{\text{x}}{3}+\frac{\text{y}}{2}=1$ is $\frac{3}{2}(\pi-2)\text{ sq.units}$
Reason: Formula to calculate the area of the smaller region bounded by the ellipse $\frac{\text{x}^2}{\text{a}^2}+\frac{\text{y}^2}{\text{b}^2}=1$ and the line $\frac{\text{x}}{\text{a}}+\frac{\text{y}}{\text{b}}=1$ is $\frac{\text{ab}}{4}(\pi-2) \text{ sq.units}$
- Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
- Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
- Assertion is correct statement but Reason is wrong statement.
- Assertion is wrong statement but Reason is correct statement.
Directions: In these questions, a statement of Assertion is followed by a statement of Reason is given.Choose the correct answer out of the following choices:
Assertion: The area of the region bounded by the curve y2 = 4x and the line x = 3 is $8\sqrt{3}$ sq. units.
Reason: The area of the region bounded by the curve x2 = 4y and the line x = 4y - 2 is $\frac{9}{8}$ sq. units.
View full solution →Assertion: The area of the region bounded by the curve y2 = 4x and the line x = 3 is $8\sqrt{3}$ sq. units.
Reason: The area of the region bounded by the curve x2 = 4y and the line x = 4y - 2 is $\frac{9}{8}$ sq. units.
- Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
- Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
- Assertion is correct statement but Reason is wrong statement.
- Assertion is wrong statement but Reason is correct statement.
Directions: In these questions, a statement of Assertion is followed by a statement of Reason is given.Choose the correct answer out of the following choices:
Asseration: Thearea bounded bythe parabola y2 = 4ax and the line x = a and x = 4a is $\frac{56\text{a}^2}{3}$ sq. units.
Reason: The area bounded by the curves y = 3x and y = x2 is 9.5 sq.units.
View full solution →Asseration: Thearea bounded bythe parabola y2 = 4ax and the line x = a and x = 4a is $\frac{56\text{a}^2}{3}$ sq. units.
Reason: The area bounded by the curves y = 3x and y = x2 is 9.5 sq.units.
- Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
- Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
- Assertion is correct statement but Reason is wrong statement.
- Assertion is wrong statement but Reason is correct statement.
Directions: In these questions, a statement of Assertion is followed by a statement of Reason is given.Choose the correct answer out of the following choices:
Assertion: The area bounded by the curves $\text{y}^2 = 4\text{a}^2(\text{x} — 1) $ and lines $\text{x}=1$ and $\text{y}=4$ a is $\frac{8\text{a}}{3}\text{sq.units}$
Reason: The area enclosed between the parabola $\text{y}=\text{x}^2-\text{x}+2$ and the line $\text{y}=\text{x+2}$ is $\frac{4}{3}\text{ sq.units}$
View full solution →Assertion: The area bounded by the curves $\text{y}^2 = 4\text{a}^2(\text{x} — 1) $ and lines $\text{x}=1$ and $\text{y}=4$ a is $\frac{8\text{a}}{3}\text{sq.units}$
Reason: The area enclosed between the parabola $\text{y}=\text{x}^2-\text{x}+2$ and the line $\text{y}=\text{x+2}$ is $\frac{4}{3}\text{ sq.units}$
- Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
- Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
- Assertion is correct statement but Reason is wrong statement.
- Assertion is wrong statement but Reason is correct statement.
The area of the region bounded by the circle x2 + y2 = 1 is:
View full solution →- $2\pi\text{ sq.}\text{ units}$
- $\pi\text{ sq.}\text{ units}$
- $3\pi\text{ sq.}\text{ units}$
- $4\pi\text{ sq.}\text{ units}$
Using integration, find area of the bounded between the line x = 2 and the parabola y2 = 8x.
Sketch the graph of $\text{y}=\sqrt{\text{x}+1}$ in [0, 4] and determine the area of the region enclosed by the curve, the x-axis and the lines x = 0, x = 4.
View full solution →If $\text{A}=\begin{bmatrix}2&3\\5&7\end{bmatrix},\text{ B}=\begin{bmatrix}-1&0&2\\3&4&1\end{bmatrix},\text{C}=\begin{bmatrix}-1&2&3\\2&1&0\end{bmatrix},$ find
A + B and B + C
View full solution →A + B and B + C
Solve the following differential equation:
View full solution →$x \cos \text{y dy} = ( xe^{x} \log x + e^{x}) dx$
Find the area bounded by the curve $\text{y}=\sin\text{x}$ between x = 0 and $\text{x}=2\pi.$
View full solution →Draw a rough sketch of the curve $\text{y}=\sqrt{\text{x}-1}$ in the interval [1, 5]. Find the area under the curve and between the lines x = 1 and x = 5.
View full solution →Find the area bounded by the curve $\text{y}=2\cos\text{x}$ and the x-axis from x = 0 to $\text{x}=2\pi.$
View full solution →Find the intervals in which the function f given by $\text{f}\text{(x)}=\text{x}^3+\frac{1}{\text{x}^3},\text{x}\neq0\text{ is}$ (i) increasing (ii) decreasing.
View full solution →Prove that the curves $\text{y}^{2} = 4x \text{ and } x^{2} = 4y $ divided the area of square bounded by $x = 0, x = 4,y=4 \text{ and } y = 0$ into three equal parts.
View full solution →Tangent to the circle $\text{x}^{2} + \text{y}^{2} = 4$ at any point on it in the first quadrant makes intercepts OA and OB on x and y axes respectively, O being the centre of the circle. Find the minimum value of (OA + OB).
View full solution →If the area bounded by the parabola $\text{y}^{2} = 16\text{ax}$ and the line $\text{y = 4 mx}$ is $\frac{\text{a}^{2}}{12}$ sq. units, then using integration, find the value of m.
View full solution →Using integration, find the area of the region bounded by the triangle whose vertices are (–1, 2), (1, 5) and (3, 4).
Prove that the curves $\text{y}^{2} = 4x \text{ and } x^{2} = 4y $ divided the area of square bounded by $x = 0, x = 4,y=4 \text{ and } y = 0$ into three equal parts.
View full solution →A child cut a pizza with a knife. Pizza is circular in shape which is represented by x2 + y2 = 4 and sharp edge of knife represents a straight line given by $\text{x}=\sqrt{3\text{y}}$ Based on the above information, answer the following questions. 
View full solution → - The point(s) of intersection of the edge of knife (line) and pizza shown in the figure is (are).
- $(1, \sqrt{3}),(-1,-\sqrt{3})$
- $(\sqrt{3},1),(-\sqrt{3,}-1)$
- $(\sqrt{2,}0),(0,\sqrt{3})$
- $(-\sqrt{3,}),(1,-\sqrt{3})$
- Which of the following shaded portion represent the smaller area bounded by pizza and edge of knife in first quadrant?
- Value of area of the region bounded by circular pizza and edge of knife in first quadrant is.
- $\frac{\pi}{2}\text{ sq.units}$
- $\frac{\pi}{3}\text{ sq.units}$
- $\frac{\pi}{5}\text{ sq.units}$
- $\pi\text{ sq.units}$
- Area of each slice of pizza when child cut the pizza into 4 equal pieces is.
- $\pi\text{ sq.units}$
- $\frac{\pi}{2}\text{ sq.units}$
- $3\pi\text{ sq.units}$
- $2\pi\text{ sq.units}$
- Area of whole pizza is.
- $3\pi\text{ sq.units}$
- $2\pi\text{ sq.units}$
- $5\pi\text{ sq.units}$
- $4\pi\text{ sq.units}$
Consider the following equations of curves x2 = y and y = x. On the basis of above information, answer the following questions.
View full solution →- The point(s) of intersection of both the curves is (are).
- (0, 0)(2, 2)
- (0, 0)(1, 1)
- (0, 0)(-1, -1)
- (0, 0)(-2, -2)
- Area bounded by the curves is represented by which of the following graph?
- The value of the integral $\int\limits_{1}^{0}\text{x}\ \text{dx}$ is.
- $\frac{1}{4}$
- $\frac{1}{3}$
- $\frac{1}{2}$
- $1$
- The value of the integral $\int\limits_{0}^{1}\text{x}^2\ \text{dx}$ is.
- $\frac{1}{4}$
- $\frac{1}{3}$
- $\frac{1}{2}$
- $1$
- The value of area bounded by the curves x2 = y and x = y is.
- $\frac{1}{6}\text{ sq}.\text{unit}$
- $\frac{1}{3}\text{ sq}.\text{unit}$
- $\frac{1}{2}\text{ sq}.\text{unit}$
- ${1}\text{ sq}.\text{unit}$
Ajay cut two circular pieces of cardboard and placed one upon other as shown in figure. One of the circle represents the equation (x - 1)2 + y2 = 1, while other circle represents the equation x2 + y2 = 1.
Based on the above information, answer the following questions.
View full solution →Based on the above information, answer the following questions.
- Both the circular pieces of cardboard meet each other at
- $\text{x}=1$
- $\text{x}=\frac{1}{2}$
- $\text{x}=\frac{1}{3}$
- $\text{x}=\frac{1}{4}$
- Graph of given two curves can be drawn as.
- None of these
- Value of $\int\limits_{0}^{\frac{1}{2}}\sqrt{1-(\text{x}-1)^2}\text{dx}$ is.
- $\frac{\pi}{6}-\frac{\sqrt{3}}{8}$
- $\frac{\pi}{6}+\frac{\sqrt{3}}{8}$
- $\frac{\pi}{2}+\frac{\sqrt{3}}{4}$
- $\frac{\pi}{2}-\frac{\sqrt{3}}{4}$
- Value of $\int\limits_{\frac{1}{2}}^{1}\sqrt{1-\text{x}^2}\text{dx}$ is.
- $\frac{\pi}{6}+\frac{\sqrt{3}}{4}$
- $\frac{\pi}{6}+\frac{\sqrt{3}}{8}$
- $\frac{\pi}{6}-\frac{\sqrt{3}}{8}$
- $\frac{\pi}{2}-\frac{\sqrt{3}}{4}$
- Area of hidden portion of lower circle is.
- $\bigg(\frac{2\pi}{3}+\frac{\sqrt{3}}{2}\bigg)\text{ sq.units}$
- $\bigg(\frac{\pi}{3}-\frac{\sqrt{3}}{8}\bigg)\text{ sq.units}$
- $\bigg(\frac{\pi}{3}+\frac{\sqrt{3}}{8}\bigg)\text{ sq.units}$
- $\bigg(\frac{2\pi}{3}-\frac{\sqrt{3}}{2}\bigg)\text{ sq.units}$
Consider the following equation of curve y2 = 4x and straight line x + y = 3.
Based on the above information, answer the following questions.
View full solution →Based on the above information, answer the following questions.
- The line x + y = 3 cuts the x-axis and y-axis respectively at.
- (0, 2), (2, 0)
- (3, 3), (0, 0)
- (0, 3), (3, 0)
- (3, 0), (0, 3)
- Point(s) of intersection of two given curves is (are).
- (1, -2), (-9, 6)
- (2, 1), (-6, 9)
- (1, 2), (9, -6)
- None of these.
- Which of the following shaded portion re present the area bounded by given curves?
- None of these
- Value of the integral $\int\limits_{-6}^{2}(3-\text{y})\text{ dy}$ is
- 10
- 20
- 30
- 40
- Value of area bounded by given curves is.
- $56\text{ sq.units}$
- $\frac{63}{5}\text{ sq. units}$
- $\frac{64}{3}\text{ sq. units}$
- $31\text{ sq.units}$
A mirror in the shape of an ellipse represented by $\frac{\text{x}^2}{9}+-\frac{\text{y}^2}{4}=1$ was hanging on the wall. Arun and his sister were playing with ball inside the house, even their mother refused to do so. All of sudden, ball hit the mirror and got a scratch in the shape of line represented by $\frac{\text{x}}{3}+\frac{\text{y}}{2}=1$ 
Based on the above information, answer the following questions.
View full solution → Based on the above information, answer the following questions. - Point(s) of intersection of ellipse and scratch (straight line) is (are).
- (0, 2), (3, 0)
- (2, 0), (3, 0)
- (2, 3), (0, 0)
- (0, 3), (3, 0)
- Area of smaller region bounded by the ellipse and line is represented by.
- The value of $\frac{2}{3}\int\limits_{0}^{3}\sqrt{9-\text{x}^2}\text{dx}$ is.
- $\frac{\pi}{2}$
- $\pi$
- $\frac{3\pi}{2}$
- $\frac{\pi}{4}$
- The value of $2\int\limits_{0}^{3}\bigg(1-\frac{\text{x}}{3}\bigg)\text{dx}$ is.
- 0
- 1
- 2
- 3
- Area of the smaller region bounded by the mirror and scratch is.
- $3\Big(\frac{\pi}{2}+1\Big)\text{ sq.units}$
- $\Big(\frac{\pi}{2}+1\Big)\text{ sq.units}$
- $\Big(\frac{\pi}{2}-1\Big)\text{ sq.units}$
- $3\Big(\frac{\pi}{2}-1\Big)\text{ sq.units}$
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