Question:
(b) The value of \( \int x \sin x \, dx \) will be:
(b) The value of \( \int x \sin x \, dx \) will be:
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When solving integrals using parts, carefully choose \( u \) and \( dv \) for easier differentiation and integration.
Updated On: Mar 1, 2025
- \(-x \cos x + \sin x + C\)
- \(x \cos x - \sin x + C\)
- \(x \sin x - \cos x + C\)
- \(-x \cos x - \sin x + C\)
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The Correct Option is A
Solution and Explanation
Usingintegrationbyparts,let:
\[
u=x\quad\text{and}\quaddv=\sinx\,dx.
\]
Then:
\[
du=dx\quad\text{and}\quadv=-\cosx.
\]
Applyingtheformula\(\intu\,dv=uv-\intv\,du\):
\[
\intx\sinx\,dx=-x\cosx+\int\cosx\,dx.
\]
\[
\intx\sinx\,dx=-x\cosx+\sinx+C.
\]
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