Integral Calculus Question 463
Question: $ \int_{{}}^{{}}{{e^{x^{2}}}x\ dx} $ is equal to
[SCRA 1996]
Options:
A) $ {e^{x^{2}}} $
B) $ \frac{1}{2}{e^{x^{2}}} $
C) $ 2{e^{x^{2}}} $
D) $ \frac{{e^{x^{2}}}-x^{2}}{2} $
Show Answer
Answer:
Correct Answer: B
Solution:
$ \int_{{}}^{{}}{{e^{x^{2}}}.x,dx}=\frac{1}{2}\int_{{}}^{{}}{(2x){e^{x^{2}}}dx} $ $ =\frac{1}{2}\int_{{}}^{{}}{e^{t}dt}=\frac{1}{2}e^{t}=\frac{1}{2}{e^{x^{2}}} $ , (Put $ x^{2}=t\Rightarrow dt=2x,dx) $ .
BETA
