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Please Solve R.D.Sharma class 12 Chapter 19 Definite Integrals Exercise 19.1 Question 7 Maths textbook Solution.

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Answer:\frac{\pi }{2}

Hint:Use indefinite formula to solve the integral and then put the value of limit to get the required answer

Given: \int_{-1}^{1}\frac{1}{1+x^{2}}dx

Solution:\int_{-1}^{1}\frac{1}{1+x^{2}}dx                            \left [ \int \frac{1}{1+x^{2}}dx=\tan ^{-1}x \right ]

=\tan ^{-1}(1)-\tan ^{-1}(-1)                                                \left[\begin{array}{l} \tan \left(\frac{\pi}{4}\right)=1 \Rightarrow \tan ^{-1}(1)=\frac{\pi}{4} \\ \tan ^{-1}(-1)=-\frac{\pi}{4} \end{array}\right]

=\left [ \frac{\pi }{4}+\frac{\pi }{4} \right ]=\frac{2\pi }{4}=\frac{\pi }{2}

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