Definite Integration Question 37
Question: The value of $ \int _{0}^{1}{|3x^{2}-1|dx} $ is
[AMU 1999]
Options:
A) 0
B) $ 4/3\sqrt{3} $
C) 3/7
D) 5/6
Show Answer
Answer:
Correct Answer: B
Solution:
$ \int _{0}^{1}{|3x^{2}-1|dx=\int _{0}^{1/\sqrt{3}}{(1-3x^{2})dx+\int _{1/\sqrt{3}}^{1}{(3x^{2}-1)dx}}} $
$ =[x-x^{3}]_0^{1/\sqrt{3}}+[x^{3}-x] _{1/\sqrt{3}}^{1} $
$ =\frac{1}{\sqrt{3}}-\frac{1}{3\sqrt{3}}+\frac{-1}{3\sqrt{3}}+\frac{1}{\sqrt{3}} $
$ =\frac{4}{3\sqrt{3}} $ .
BETA
