Q239 / 270 · NDA 2024 (Phase 1) · Mathematics

Let $\varphi(a)=\int_a^{a+100 \pi}|\sin x| d x$ What is $\varphi(a)$ equal to?

  • A
    0
  • B
    $a$
  • C
    $100 a$
  • Correct answer
    D
    200

Solution

$\phi(a)=\int_a^{a+100 \pi}|\sin x| d x$ As period of $|\sin x|=\pi$ and $|\sin x|=\sin x$ in $\begin{aligned} \phi(a) & =\int_0^{100 \pi}|\sin x| d x \\ & =100 \int_0^\pi|\sin x| d x \\ & =100 \int_0^\pi \sin x d x \\ \phi(a) & =100(-\cos x)_0^\pi=100 \times 2=200 \end{aligned}$

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

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