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Indefinite Integrals — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsIndefinite Integrals2 Marks
Question
Evaluate the following integrals:
$\int\text{x}\cos\text{x dx}$
✓

Answer

Let $\text{I}=\int\text{x}\cos\text{x dx}$
Using integration by parts,
$\text{I}=\text{x}\int\cos\text{x dx}-\int(1\times\int\cos\text{x dx})\text{dx+C}$
$=\text{x}\sin\text{x}-\int\sin\text{x dx+C}$
$\text{I}=\text{x}\sin\text{x}+\cos\text{x+C}$

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