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  • Explain solution RD Sharma class 12 chapter 19 Definite Integrals exercise Very short answer type question 12 maths

Explain solution RD Sharma class 12 chapter 19 Definite Integrals exercise Very short answer type question 12 maths

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Answer: \frac{\pi }{12}

Hint: You must know the integration rules of trigonometric function with its limits


Given: \int_{0}^{3} \frac{1}{x^{2}+9} d x

Solution:  \int_{0}^{3} \frac{1}{x^{2}+9} d x

Use the formula \int \frac{1}{x^{2}+a^{2}} d x=\frac{1}{a} \tan ^{-1} \frac{x}{a}+c

\begin{aligned} &=\frac{1}{3}\left[\tan ^{-1} \frac{x}{3}\right]_{0}^{3} \\\\ &=\frac{1}{3}\left[\tan ^{-1} 1-\tan ^{-1} 0\right] \end{aligned}

\begin{aligned} &=\frac{1}{3}\left[\frac{\pi}{4}\right] \\\\ &=\frac{\pi}{12} \end{aligned}

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