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Model Paper 2 — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsModel Paper 22 Marks
Question
Integrate the function $e^x(\sin x+\cos x)$
✓

Answer

$I=\int e^x(\sin x+\cos x) d x$
Now,
Let $\sin x = f ( x ) \Rightarrow f ^{\prime}( x )=\cos x$
We know that,
$\int e^x\left\{f(x)+f^{\prime}(x)\right\} d x=e^x f(x)+c$
Thus,
$\int e^x(\sin x+\cos x) d x=e^x \sin x+C$

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