_0^1 e^ 2 , In ,x ,dx = - Vidyadip

MCQ

$\int_0^1 {{e^{2\,{\rm{In}}\,x}}\,dx} = $

A
$0$
B
$\frac{1}{2}$
✓
$\frac{1}{3}$
D
$\frac{1}{4}$

✓

Answer

Correct option: C.

$\frac{1}{3}$

c
(c)$\int_0^1 {{e^{2\log x}}dx = \int_0^1 {{e^{\log {x^2}}}} dx = \int_0^1 {{x^2}dx = \left[ {\frac{{{x^3}}}{3}} \right]_0^1 = \frac{1}{3}} } $.

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 "M.C.Q (1 Marks)" from STD 12 - 7.2 definite integral→STD 12 - 7.2 definite integral — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

The function $f(x) = x − [x],$ where $[⋅]$ denotes the greatest integer function is :

If $\text{A}=\begin{bmatrix} 2 & -1 \\ 3 & -2 \end{bmatrix},$ then $A^n =$

Choose the correct answer from the given four options. A box contains 3 orange balls, 3 green balls and 2 blue balls. Three balls are drawn at random from the box without replacement. The probability of drawing 2 green balls and one blue ball is:

The solution of the equation $\frac{{{d^2}y}}{{d{x^2}}} = {e^{ - 2x}}$ is

The value of the integral $\int_0^{\frac{\pi}{4}} \frac{x d x}{\sin ^4(2 x)+\cos ^4(2 x)}$ equals :

Find area of the triangle with vertices at the point given in each of the following: $(1,0),(6,0),(4,3)$

For any $2 \times 2$ matrix $P$, which of the following matrices can be $Q$ such that $P Q=Q P$ ?

The area of the portion of the circle $x^2+y^2=1,$ which lies inside the parabola $y^2=1-x,$ is:

Let $O$ be the origin and $\overline{ OA }=2 \hat{ i }+2 \hat{ j }+\hat{ k }, \overline{ OB }=\hat{ i }-2 \hat{ j }+2 \hat{ k }$ and $\overline{ OC }=\frac{1}{2}(\overline{ OB }-\lambda \overline{ OA })$ for some $\lambda>0$. If $|\overline{ OB } \times \overline{ OC }|=\frac{9}{2}$, then which of the following statements is (are) TRUE?

$(A)$ Projection of $\overline{ OC }$ on $\overline{ OA }$ is $-\frac{3}{2}$

$(B)$ Area of the triangle $OAB$ is $\frac{9}{2}$

$(C)$ Area of the triangle $ABC$ is $\frac{9}{2}$

$(D)$ The acute angle between the diagonals of the parallelogram with adjacent sides $\overline{ OA }$ and $\overline{ OC }$ is $\frac{\pi}{3}$

If $AB = C$, then matrices $A,B,C$are