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Question Number 117002 by TANMAY PANACEA last updated on 08/Oct/20

$${\int }_0^{n\pi +v}\mid sinx\mid dx$$

Answered by TANMAY PANACEA last updated on 08/Oct/20

$$\mid sinx\mid isalsays+veandeachloopareaof$$$$sinxis2★★$$$${\int }_0^{\pi }sinxdx=-\mid cosx{\mid }_0^{\pi }=2$$$$★★$$$$nowlook$$$${\int }_0^{n\pi +v}\mid sinx\mid dx={\int }_0^v\mid sinx\mid dx+{\int }_v^{n\pi +v}\mid sinx\mid dx$$$$here0<v<\pi$$$${\int }_0^{v}sinxdx=-\mid cosx{\mid }_0^v=-(cozv-1)=1-cosv$$$${\int }_v^{n\pi +v}\mid sinx\mid dx\to inintervalvtov+n\pi$$$$numberofloopso$$$${\int }_v^{n\pi +v}\mid sinx\mid dx=n\times 2=2n$$$$\mathit{I}=2n+1-cosv$$$$plzcheck$$

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