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Definite Integrals — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDefinite Integrals2 Marks
Question
Evaluate the following integrals:
$\int\limits^\frac{\pi}{2}_{-\frac{\pi}{2}}\text{x}\cos^2\text{x}\text{ dx}$
✓

Answer

$\int\limits^\frac{\pi}{4}_0\tan^2\text{x}\text{ dx}$
$=\int\limits^\frac{\pi}{2}_0(\sec^2\text{x}-1)\text{dx}$
$=\big[\tan\text{x}-\text{x}\big]^\frac{\pi}{4}_0$
$=1-\frac{\pi}{4}-0$
$=1-\frac{\pi}{4}$

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