Definite Integration Question 311
Question: The area of the region bounded by the curve $ y=x|x| $ , x-axis and the ordinates $ x=1,x=-1 $ is given by
[Pb. CET 2004]
Options:
A) Zero
B) $ \frac{1}{3} $
C) $ \frac{2}{3} $
1
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Answer:
Correct Answer: C
Solution:
Required area $ =\int _{-1}^{1}{x|x|dx} $
$ =\int _{-1}^{0}{-x^{2}dx+\int_0^{1}{x^{2}dx}} $
= $ ( \frac{-x^{3}}{3} ) _{-1}^{0} $
$ +( \frac{x^{3}}{3} )_0^{1} $
$ =| \frac{-1}{3} |+| \frac{1}{3} |=\frac{2}{3} $ .
BETA
