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  • Need solution for RD Sharma Maths Class 12 Chapter 18 Indefinite Integrals Excercise Very Short Answers Question 41

Need solution for RD Sharma Maths Class 12 Chapter 18 Indefinite Integrals Excercise Very Short Answers Question 41

Answers (1)

best_answer

Answer: -2\cos \sqrt{x}+c

Hint: You must know about the integral rule of trigonometric functions

Given: \int \frac{\sin\sqrt{x}}{\sqrt{x}}dx

Solution:

\int \frac{\sin\sqrt{x}}{\sqrt{x}}dx

Let

\begin{aligned} &t=\cos \sqrt{x}\\ &d t=-\frac{\sin \sqrt{x}}{2 \sqrt{x}} d x\\ &-2 d t=\frac{\sin \sqrt{x}}{\sqrt{x}} d x \quad\quad\quad\quad\quad\quad\quad\quad\left[\frac{d}{d x} \cos x=-\sin x\right] \end{aligned}

\begin{aligned} &\int \frac{\sin \sqrt{x}}{\sqrt{x}} d x=\int-2 d t \\ &=-2 \mathrm{t}+\mathrm{c}\quad\quad\quad\quad\quad\quad\quad \quad\left[\int x^{n} d x=\frac{x^{n+1}}{n+1}\right] \\ &=-2 \cos \sqrt{x}+c \end{aligned}

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