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Integrals — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsIntegrals2 Marks
Question
Evaluate the definite integral $\int_0^{\frac{\pi}{4}} \tan x d x$.
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Answer

$\int _ { 0 } ^ { \pi / 4 } \tan x d x = [ \log | \sec x | ] _ { 0 } ^ { \pi / 4 }$
${ = \log \left| \sec \frac { \pi } { 4 } \right| - \log | \sec 0 | } \\ $
${ = \log | \sqrt { 2 } | - \log | 1 | } $
$\\ { = \frac { 1 } { 2 } \log 2 } $

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