Definite Integration Question 117
Question: . The integral value $ \int _{-2}^{0}{[ x^{3}+3x^{2}+3x+3+(x+1)\cos (x+1) ]\ dx} $ is
[IIT Screening 2005]
Options:
A) 2
B) 4
C) 0
D) 8
Show Answer
Answer:
Correct Answer: B
Solution:
Let $ x+1=t $ when $ x=-2\to 0 $ , then $ t=-1\to 1 $
$ I=\int _{-1}^{1}{(t^{3}+2+t\cos t)\ dt} $
$Since\ t^{3}\text{and }t\ cost $ are odd functions
$ \therefore $ $ I=\int _{-1}^{1}{2dt=[2t] _{-1}^{1}=4} $ .
BETA
