Definite Integration Question 433
Question: The area bounded by the curve y = x $ | x | $ , x-axis and the ordinates x = 1, $ x=-1 $ is given by
Options:
A) 0
B) 1/3
C) 2/3
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
[c] Required area $ =| \int _{-1}^{0}{x|x|dx} | $
$ =| | \int _{-1}^{0}{x|x|dx} | |+| \int_1^{0}{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} ]}^{1}}_0=\frac{1}{3}+\frac{1}{3}+\frac{2}{3} $
BETA
