_ ^ e^ x^2 x ;dx is equal to - Vidyadip

MCQ

$\int_{}^{} {{e^{{x^2}}}x\;dx} $ is equal to

A
${e^{{x^2}}}$
✓
$\frac{1}{2}{e^{{x^2}}}$
C
$2{e^{{x^2}}}$
D
$\frac{{{e^{{x^2}}} - {x^2}}}{2}$

✓

Answer

Correct option: B.

$\frac{1}{2}{e^{{x^2}}}$

b
(b)$\int_{}^{} {{e^{{x^2}}}.x\,dx} = \frac{1}{2}\int_{}^{} {(2x){e^{{x^2}}}dx} $

(Put ${x^2} = t \Rightarrow dt = 2x\,dx)$.

$ = \frac{1}{2}\int_{}^{} {{e^t}dt} = \frac{1}{2}{e^t} = \frac{1}{2}{e^{{x^2}}}$,

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 7.1 inderfinite integral→7.1 inderfinite integral — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

$\int_{0}^{\pi /2}{\frac{dx}{{{a}^{2}}{{\cos }^{2}}x+{{b}^{2}}{{\sin }^{2}}x}}\,=$

Lety = $f(x) =\left[ \begin{array}{l}
\,\,\,\,{e^{ - \,\,\,\frac{1}{{{x^2}}}}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,if\,\,\,\,\,x\,\,\,\, \ne \,\,\,0\\
\,\,\,\,0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,if\,\,\,\,x\,\,\,\, = \,\,\,0
\end{array} \right.$ Then which of the following can best represent the graph of $y = f(x)$ ?

Area bounded by lines $y = 2 + x,$ $y = 2 - x$ and $x = 2$ is

A random variable X has the following probability distribution:

X:	1	2	3	4	5	6	7	8
P(X):	0.15	0.23	0.12	0.10	0.20	0.08	0.07	0.05

Find the events E = {X : X is a prime number}, F{X : X < 4}, the probability $\text{P}(\text{E}\cup\text{F})$ is:

Solution of $ydx - xdy = {x^2}ydx$ is

The distance of the plane through the intersection of the planes ax + by + cz +d = 0 and lx + my + nz + P = 0 and parallel to the line y = 0, z = 0

(bl - am)y + (cl - an)z + dl - ap = 0
(am - bl)x + (mc - bn)z + md - bp = 0
(na - cl)x + (bn - cm)y + nd - cp = 0
None of these

Let $\quad \mathrm{f}: \mathbb{R}-\{0\} \rightarrow \mathbb{R}$ be a function satisfying $f\left(\frac{x}{y}\right)=\frac{f(x)}{f(y)}$ for all $x, y, f(y) \neq 0$. If $f^{\prime}(1)=2024$ then

If ${\rm{f}}\left( x \right) = \int\limits_{^{{\pi ^2}/16}}^{{x^2}} {\frac{{\sin x\,\cdot\sin \sqrt \theta }}{{1 + {{\cos }^2}\sqrt \theta }}} .d\theta $ then the value of $f ‘$$\left( {\frac{\pi }{2}} \right)$ , is

If $f(x)=\int_{0}^{x}(5+|1-t|) d t, \quad x>2$

$\quad \quad \quad \quad \quad 5 x+1,\quad \quad \quad \quad \quad x \leq 2$, then

Consider the function $f(x) = {e^{ - 2x}}$ $sin\, 2x$ over the interval $\left( {0,{\pi \over 2}} \right)$. A real number $c \in \left( {0,{\pi \over 2}} \right)\,,$ as guaranteed by Rolle’s theorem, such that $f'\,(c) = 0$ is