The value of _ ,0 ^ ,1 ,| ,3 x^2 - 1 ,| ,dx is - Vidyadip

MCQ

The value of $\int_{\,0}^{\,1} {\,|\,3{x^2} - 1\,|\,dx} $ is

A
$0$
✓
$4/(3\sqrt 3) $
C
$3/7$
D
$5/6$

✓

Answer

Correct option: B.

$4/(3\sqrt 3) $

b
(b) $\int_{\,0}^{\,1} {|3{x^2} - 1|dx = \int_{\,0}^{\,1/\sqrt 3 } {(1 - 3{x^2})dx + \int_{\,1/\sqrt 3 }^{\,1} {(3{x^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 }}$.

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