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Chapter 4: Q. 12 (page 362)

Show that F(x)=sinx-xcosx+2 is an antiderivative of f(x)=sinx.

Short Answer

Expert verified

It is shown thatF(x)=sinx-xcosx+2is an antiderivative off(x)=sinx.

Step by step solution

01

Step 1. Given Information.

The given derivative isF(x)=sinx-xcosx+2and the given function isf(x)=sinx.

02

Step 2. Differentiation.

On differentiating the function,

We get,

ddxxsinx=1(sinx)-x(cosx)=sinx-xcosxSo,鈭�xsinxdx=sinx-xcosx+CTherefore,F(x)=sinx-xcosx+2isananti-derivativeoff(x)=xsinx.

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