The value of _0^1 |3 x^2-1 | d x is - Vidyadip

MCQ

The value of $\int_0^1\left|3 x^2-1\right| d x$ is

A
$0$
✓
$\frac{4}{3 \sqrt{3}}$
C
$\frac{3}{7}$
D
$\frac{5}{6}$

✓

Answer

Correct option: B.

$\frac{4}{3 \sqrt{3}}$

(B)
$\int_0^1\left|3 x^2-1\right| d x=\int_0^{\frac{1}{\sqrt{3}}}\left(1-3 x^2\right) d x+\int_{\frac{1}{\sqrt{3}}}^1\left(3 x^2-1\right) d x$
$\begin{array}{l}=\left[x-x^3\right]_0^{1 / \sqrt{3}}+\left[x^3-x\right]_{1 / \sqrt{3}}^1 \\ =\frac{1}{\sqrt{3}}-\frac{1}{3 \sqrt{3}}-\frac{1}{3 \sqrt{3}}+\frac{1}{\sqrt{3}}=\frac{4}{3 \sqrt{3}}\end{array}$

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