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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Definite Integration

NDA 2023 · Mathematics · Definite Integration

What is ∫_0^ 8 π | x| d x equal to?

What is ∫08π∣sin⁡x∣dx\int_0^{8 \pi}|\sin x| d x equal to?

Options

  1. A2
  2. B4
  3. C8
  4. D16

Correct answer

D. 16

Step-by-step solution

Since, ∣sin⁡x∣|\sin \mathrm{x}| is periodic function with period π\pi So, ∫08π∣sin⁡x∣dx=8∫0π∣sin⁡x∣dx=8∫0π∣sin⁡x∣dx=0=8(−cos⁡x)0π=8(+1+1)=16\begin{aligned} & \text{ So, } \int_0^{8 \pi}|\sin x| d x=8 \int_0^\pi|\sin x| d x \\ & \quad=8 \int_0^\pi|\sin x| d x=0 \\ & \quad=8(-\cos x)_0^\pi=8(+1+1)=16 \end{aligned}$$
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