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NDA 2019
Exam
NDA
Year
2019
Subject
Mathematics
Chapter
Definite Integration

NDA 2019 · Mathematics · Definite Integration

Paragraph: Consider the integrals I_1=∫_0^x (x d x)/(1+ x) and I...

Paragraph: Consider the integrals I1=∫0xxdx1+sin⁡x and \mathrm{I}_1=\int_0^x \frac{x d x}{1+\sin x} \text{ and }\mathrm{I}2=∫0π(π−x)dx1−sin⁡(π+x)_2=\int_0^\pi \frac{(\pi-x) d x}{1-\sin (\pi+x)}Question: What is the value of I1+\mathrm{I}_1+\mathrm{I}2?_2 ?

Options

  1. A2π2 \pi
  2. Bπ\pi
  3. Cπ2\frac{\pi}{2}
  4. D0

Correct answer

A. 2π2 \pi

Step-by-step solution

∵I1=I2∴I1+I2=π+π=2π\begin{aligned} & \because I_1=I_2 \\ & \therefore I_1+I_2=\pi+\pi=2 \pi\end{aligned}
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