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Definite Integrals — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDefinite Integrals2 Marks
Question
Evaluate the following integrals:
$\int\limits^\frac{\pi}{4}_0\sin2\text{x dx}$
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Answer

$\int\limits^\frac{\pi}{4}_0\sin2\text{x dx}$
$=\Big[\frac{-\cos2\text{x}}{2}\Big]^{\frac{\pi}{4}}_0$
$=-\frac{1}{2}\Big(\cos\frac{\pi}{2}-\cos0\Big)$
$=-\frac{1}{2}\times(0-1)$
$=\frac{1}{2}$

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