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NDA 2013
Exam
NDA
Year
2013
Subject
Mathematics
Chapter
Indefinite Integration

NDA 2013 · Mathematics · Indefinite Integration

What is ∫(x x+ x) d x equal to? where c is an arbitrary constant.

What is ∫(xcos⁡x+sin⁡x)dx\int(x \cos x+\sin x) d x equal to? where c is an arbitrary constant.

Options

  1. Ax \sin x+c
  2. Bx \cos x+c
  3. C–x \sin x +c
  4. D–x \cos x +c

Correct answer

A. x \sin x+c

Step-by-step solution

∫(xcos⁡x+sin⁡x)⋅dx=∫xcos⁡x⋅dx+∫sin⁡x⋅dx=x⋅sin⁡x+cos⁡x−cos⁡x+C=xsin⁡x+C\begin{aligned} & \int(x \cos x+\sin x) \cdot d x \\ & =\int x \cos x \cdot d x+\int \sin x \cdot d x \\ & =x \cdot \sin x+\cos x-\cos x+C \\ & =x \sin x+C\end{aligned}
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