Math, asked by kumarutsav8695, 1 year ago

Integration of (xsinpix

Answers

Answered by joeljovision85
0
write the whole question
Answered by Anonymous
101

♣ Qᴜᴇꜱᴛɪᴏɴ :

\large\boxed{\sf{\int \:xsin\left(x\right)dx}}

♣ ᴀɴꜱᴡᴇʀ :

\large\boxed{\sf{\int \:x\sin \left(x\right)dx=-x\cos \left(x\right)+\sin \left(x\right)+C}}

♣ ᴄᴀʟᴄᴜʟᴀᴛɪᴏɴꜱ :

\text { Apply Integration By Parts: } u=x, v^{\prime}=\sin (x)

\sf{=-x\cos \left(x\right)-\int \:-\cos \left(x\right)dx}

\sf{\int-\cos (x) d x=-\sin (x)}

\sf{=-x\cos \left(x\right)-\left(-\sin \left(x\right)\right)}

\sf{=-x\cos \left(x\right)+\sin \left(x\right)}

\mathrm{Add\:a\:constant\:to\:the\:solution}

\large\boxed{\sf{=-x\cos \left(x\right)+\sin \left(x\right)+C}}

Similar questions