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Definite Integrals — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDefinite Integrals2 Marks
Question
Evaluate the following definite integrals:
$\int_{0}^\limits{\frac{\pi}{2}}(\sin\text{x}+\cos\text{x})\text{dx}$
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Answer

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

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