Definite Integration Question 166
Question: The area between the parabola $ y=x^{2} $ and the line $ y=x $ is
[UPSEAT 2004]
Options:
A) $ \frac{1}{6} $ sq. unit
B) $ \frac{1}{3} $ sq. unit
C) $ \frac{1}{2} $ sq. unit
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
Given curves are $ y=x^{2} $ and $ y=x $
On solving, we get $ x=0 $ , $ x=1 $ Therefore, required area $ A=\int_0^{1}{(x^{2}-x)}dx $
$ =[ \frac{x^{3}}{3}-\frac{x^{2}}{2} ]_0^{1} $
$ =\frac{1}{3}-\frac{1}{2}=\frac{1}{6} $ sq. unit.
BETA
