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INTEGRALS — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSINTEGRALS2 Marks
Question
Evaluate the following integrals:
$\int\limits^\frac{\pi}{4}_0\tan\text{x dx}$
✓

Answer

$\int\limits^\frac{\pi}{4}_0\tan\text{x dx}$
$=\big[\log\sec\text{x}\big]^{\frac{\pi}{4}}_0$
$=\log\sec\frac{\pi}{4}-\log\sec0$
$=\log\sqrt{2}-\log1$
$=\log2^{\frac{1}{2}}-0$
$=\frac{1}{2}\log2$

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