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Chapter 4: Q. 78 (page 363)

ThefunctionsF,GaredifferentiablealsoF(x)=G(x).Where,Cisanyconstant.provethatG(x)=F(x)+C.

Short Answer

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Proved

Step by step solution

01

Step 1. To Prove

G(x)=F(x)+C.

02

Step 2. Proving

Now,F'(x)=G(x)鈭�F(x)dx=鈭�G(x)dxF(x)+C鈧�=G(x)+C鈧�G(x)=F(x)+(C鈧�-C鈧�)G(x)=F(x)+CTherefore,itisprovedthatG(x)=F(x)+C.

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