Download App

INTEGRALS — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSINTEGRALS2 Marks
Question
Integrate the function in Exercise:
$\frac{\text{e}^{5\log\text{x}}-\text{e}^{4\log\text{x}}}{\text{e}^{3\log\text{x}}-\text{e}^{2\log\text{x}}}$
✓

Answer

$\frac{\text{e}^{5\log\text{x}}-\text{e}^{4\log\text{x}}}{\text{e}^{3\log\text{x}}-\text{e}^{2\log\text{x}}}=\frac{\text{e}^{4\log\text{x}}\big(\text{e}^{\log\text{x}}-1\big)}{\text{e}^{2\log\text{x}}\big(\text{e}^{\log\text{x}}-1\big)}$$=\text{e}^{2\log\text{x}}$
$=\text{e}^{\log\text{x}^{2}}$
$=\text{x}^{2}$
$\therefore\int\frac{\text{e}^{5\log\text{x}}-\text{e}^{4\log\text{x}}}{\text{e}^{3\log\text{x}}-\text{e}^{2\log\text{x}}}\text{dx}=\int\text{x}^{2}\text{dx}=\frac{\text{x}^{3}}{3}+\text{C}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "2 Marks Questions" from INTEGRALS→INTEGRALS — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

For what valuse of $x$ and $y$ are the following matrices equal?
$\text{A}=\begin{bmatrix}2\text{x}+1&2\text{y}\\0&\text{y}^2-5\text{y}\end{bmatrix}\text{B}=\begin{bmatrix}\text{x}+3&\text{y}^2+2\\0&-6\end{bmatrix}$
→
Find the position vector of the mid point of the vector joining the points P(2, 3, 4) and Q(4, 1, –2).
→
A card is drawn from a well-shulffled deck of 52 cards. The outcome is noted, the card is replaced and the deck reshuffled. Another card is then drawn from the deck.
What is the probability that the first card is an ace and the second card is a red queen?
→
Let A = {1, 2, 3} and R = {(1, 2), (1, 1), (2, 3)} be a relation on A. What minimum number of ordered pairs may be added to R so that it may become a transitive relation on A.
→
The volume of a cube is increasing at the rate of $8 \ cm^3/ \sec$. How fast is the surface area increasing when the length of an edge is $12 \ cm$?
→
If A is a square matrix such that A (adj A) = 5I, where I denotes the identity matrix of the same order. Then, find the value of |A|.
→
Find the equation of a curve passing through the point (0, –2) given that at any point (x, y) on the curve, the product of the slope of its tangent and y coordinate of the point is equal to the x coordinate of the point.
→
Write the value of the determinant $\begin{vmatrix}\text{a}&1&\text{b}+\text{c}\\\text{b}&1&\text{c}+\text{a}\\\text{c}&1&\text{a}+\text{b}\end{vmatrix}$
→
Form the differential equation from the following primitives where constants are arbitrart:$\text{y}=\text{cx}+2\text{c}^2+\text{c}$
→
Integrate the function in Exercise:
$\frac{\text{x}^{3}}{\sqrt{1-\text{x}^{8}}}$
→