Application of Integrals - Gujarat Board (GSEB) STD 12 Science Maths Questions

Q 1M.C.Q (1 Marks)1 Mark

The area of the region bounded by the circle $x^2+y^2$ $=9$ in the first quadrant is :

A
$9 \pi$
B
$\frac{3 \pi}{4}$
✓
$\frac{9 \pi}{4}$
D
$3 \pi$

Answer: C.

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Q 2M.C.Q (1 Marks)1 Mark

Area bounded by curve $y^2=4 x, y$-axis and line $y=3$ is:

A
2
✓
$\frac{9}{4}$
C
$\frac{9}{3}$
D
$\frac{9}{2}$.

Answer: B.

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Q 3M.C.Q (1 Marks)1 Mark

Area of circle $x^2+y^2=4$ :

A
$2 \pi$
B
$16 \pi$
✓
$4 \pi$
D
$\frac{\pi}{4}$

Answer: C.

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Q 4M.C.Q (1 Marks)1 Mark

The area of the region bounded by the curve $y=x^2$ and line $y=4$ is:

A
$\frac{33}{2}$
B
$\frac{8}{3}$
C
$\frac{32}{3}$
D
$\frac{4}{3}$

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Q 5M.C.Q (1 Marks)1 Mark

The whole area of the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$ is :

A
$\pi$ square units
B
$5 \pi$ square units
C
$40 \pi$ square units
✓
$20 \pi$ square units.

Answer: D.

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Q 61 Marks1 Mark

Find the area of the region bounded by the curve $y=m x, x$-axis and the ordinates $x=0$ and $x=4$.

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Q 71 Marks1 Mark

Find the area of the region bounded by the curve $y=\cos x$ and the $x$-axis when $0 \leq x \leq \pi$.

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Q 81 Marks1 Mark

Find the area of the region bounded by the curve $y=x^2$ and the lines $x=0$ and $x=2$.

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Q 91 Marks1 Mark

Find the area bounded by the curve $y=\sin x$, the ordinate $x=\frac{\pi}{2}$ and the $x$-axis.

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Q 101 Marks1 Mark

In the interval $\left[0, \frac{\pi}{2}\right]$, find the area of the region bounded by the curve $y =\cos x$ and the $x$-axis.

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Q 112 Marks2 Marks

Find the area of the region bounded by the curve $y^2=9 x, x=2, x=4$ and the $x$-axis in the first quadrant.

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Q 122 Marks2 Marks

Find the area of the region bounded by the parabola $y^2=4 a x$ and its latus rectum.

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Q 132 Marks2 Marks

Find the area of the region bounded by $y=|x|$, $x =-3, x =1$ and the $x$-axis.

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Q 142 Marks2 Marks

Find the area bounded by the curve $y=x^3-6 x^2+$ $8 x, x=a, x=b$ and the $x$-axis.

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Q 152 Marks2 Marks

Find the area of the region bounded by $y=x$, the $x$-axis, $x=-1$ and $x=2$.

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Q 163 Marks3 Marks

Find the area of the region bounded by the curve $y=\sin 2 x+\cos 2 x$ and $x=0$ and $x=\frac{\pi}{4}$.

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Q 173 Marks3 Marks

Find the area enclosed by the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$. Draw the figure.

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Application of Integrals question types

Application of Integrals questions

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Application of Integrals Maths - Application of Integrals

Application of Integrals question types

Application of Integrals questions

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