Definite Integration Question 34
Question: $ \int _{0}^{3}{|2-x|dx} $ equals
[RPET 1999]
Options:
A) 2/7
B) 5/2
C) 3/2
D) $ -3/2 $
Show Answer
Answer:
Correct Answer: B
Solution:
$ I=\int_0^{3}{|2-x|dx} $
$ =\int_0^{2}{(2-x)}dx+\int_2^{3}{-(2-x)dx} $
$ =\int_0^{2}{(2-x)}dx-\int_2^{3}{(2-x)dx}=[ 2x-\frac{x^{2}}{2} ]_0^{2}-[ 2x-\frac{x^{2}}{2} ]_2^{3} $
$ \int_0^{\pi }{| {{\sin }^{4}}x |dx=2\int_0^{\pi /2}{{{\sin }^{4}}xdx}} $
$ =2-[ 4-\frac{9}{2} ] $
$ =\frac{5}{2} $ .
BETA
