Definite Integration Question 353
Question: The value of $ \int_0^{1}{x^{2}e^{x}dx} $ is equal to
[Pb. CET 2002]
Options:
A) $ e-2 $
B) $ e+2 $
C) $ e^{2}-2 $
D) $ e^{2} $
Show Answer
Answer:
Correct Answer: A
Solution:
We have, $ I=\int_0^{1}{x^{2}e^{x}dx} $
therefore $ I=[x^{2}.e^{x}]_0^{1}-\int_0^{1}{2x.e^{x}dx} $
therefore $ I=e-2[xe^{x}-e^{x}]_0^{1} $
therefore $ I=e-2[e-e-(0-1)] $
therefore $ I=e-2 $ .
BETA
