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Definite Integrals — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsDefinite Integrals2 Marks
Question
Evaluate the following definite integrals:$\int_{0}^\limits{1}\frac{1}{1+\text{x}^2} \text{ dx}$
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Answer

Let $\text{I}=\int_{0}^\limits{1}\frac{1}{1+\text{x}^2} \text{ dx}$ Then,$\text{I}=\big[\tan^{-1}\text{x}\big]^1_0$
$\Rightarrow\text{I}=\tan^{-1}1-\tan^{-1}0$
$\Rightarrow\text{I}=\frac{\pi}{4}-0$
$\Rightarrow\text{I}=\frac{\pi}{4}$

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