Definite Integration Question 51
Question: If $ f(x)= \begin{matrix} {e^{\cos x}}\sin x, & |x|\le 2 \\ 2, & otherwise \\ \end{matrix} . $ , then $ \int _{-2}^{3}{f(x)dx} $ is equal to
[IIT Screening 2000]
Options:
A) 0
B) 1
C) 2
D) 3
Show Answer
Answer:
Correct Answer: C
Solution:
$ \int _{-2}^{3}{f(x)dx=}\int _{-2}^{2}{f(x)dx+\int_2^{3}{f(x)dx}} $
$ \because $ $ {e^{\cos x}}\sin x $ is an odd function
$ \therefore \int _{-2}^{3}{f(x)dx}=\int _{-2}^{2}{{e^{\cos x}}\sin xdx+\int_2^{3}{2dx=0+2(3-2)=2}} $ .
BETA
