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Chapter 4: Q. 14 (page 362)

Verify that鈭�cotxdx=ln(sinx)+C. (Do not try to solve the integral from scratch.)

Short Answer

Expert verified

It is verified that鈭�cotxdx=ln(sinx)+C.

Step by step solution

01

Step 1. Given information.

The given integral is鈭�cotxdx=ln(sinx)+C.

02

Step 2. Verification.

We can write the differentiation as,

ddxln(sinx)=1sinx(cosx)

=cosxsinx=cotx

Hence, ln(sinx)is an anti-derivative ofcotx.

Therefore,

鈭�cotxdx=ln(sinx)+C

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