Q250 / 270 · NDA 2016 (Phase 2) · Mathematics

What is $\int_1^3\left|1-\mathrm{x}^4\right| \mathrm{dx}$ equal to?

  • A
    $-232 / 5$
  • B
    $-116 / 5$
  • C
    $116 / 5$
  • Correct answer
    D
    $232 / 5$

Solution

$\begin{aligned} & I=\int_1^3\left|1-x^4\right| d x \\ & I=\int_1^3-\left(1-x^4\right) d x \quad\left(\because|x|=\left\{\begin{array}{cc}x, & x \geq 0 \\ -x, & x \lt 0\end{array}\right)\right. \\ & I=\int_1^3\left(x^4-1\right) d x \Rightarrow I=\left[\frac{x^5}{5}-x\right]_1^3 \\ & I=\left(\frac{3^5}{5}-3\right)-\left(\frac{1^5}{5}-1\right) \Rightarrow I=\frac{232}{5}\end{aligned}$

Hence, the correct answer is option: 'D'.

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