Evaluate the integral. ∫sin⁡01+cos20d0

Question

Evaluate the integral.  ∫sin⁡01+cos20d0

opsadnojD · Accepted Answer

Step 1
To Determine:
Find or evaluate the integral
Given: we have an integral

\int \frac{\sin 0}{1 + \cos^{2} 0} d 0

Explanation: we have

\int \frac{\sin 0}{1 + \cos^{2} 0} d 0

let us consider

t = \cos 0 \Rightarrow d t = - \sin 0 d 0

so the integral becomes

- \int \frac{1}{1 + t^{2}} = - \tan^{- 1} t + c

Step 2
now putting the value of t then we have

\int \frac{\sin 0}{1 + \cos^{2} 0} d 0 = - \tan^{- 1} (\cos 0) + c

Answered question