Definite Integration Question 88
Question: The value of $ \int _{-2}^{3}{|1-x^{2}|dx} $ is
[AIEEE 2004]
Options:
A) $ \frac{1}{3} $
B) $ \frac{14}{3} $
C) $ \frac{7}{3} $
D) $ \frac{28}{3} $
Show Answer
Answer:
Correct Answer: D
Solution:
$ \int _{-2}^{3}{|1-x^{2}|dx=\int _{-2}^{-1}{(x^{2}-1)dx+\int _{-1}^{1}{(1-x^{2})dx+\int_1^{3}{(x^{2}-1)dx}}}} $
= $ [ \frac{x^{2}}{3}-x ] _{-2}^{-1}+[ x-\frac{x^{2}}{3} ] _{-1}^{1}+[ \frac{x^{2}}{3}-x ]_1^{2} $
$ =\frac{2}{3}+\frac{2}{3}+2( \frac{2}{3} )+(9-3)-( \frac{1}{3}-1 ) $
$ =\frac{10}{3}+6=\frac{28}{3} $ .
BETA
