Caelan

2021-11-07

Evaluate the integral.

$\int \frac{\mathrm{sin}0}{1+{\mathrm{cos}}^{2}0}d0$

opsadnojD

Skilled2021-11-08Added 95 answers

Step 1

To Determine:

Find or evaluate the integral

Given: we have an integral$\int \frac{\mathrm{sin}0}{1+{\mathrm{cos}}^{2}0}d0$

Explanation: we have$\int \frac{\mathrm{sin}0}{1+{\mathrm{cos}}^{2}0}d0$

let us consider$t=\mathrm{cos}0\Rightarrow dt=-\mathrm{sin}0d0$

so the integral becomes

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

Step 2

now putting the value of t then we have

$\int \frac{\mathrm{sin}0}{1+{\mathrm{cos}}^{2}0}d0=-{\mathrm{tan}}^{-1}\left(\mathrm{cos}0\right)+c$

To Determine:

Find or evaluate the integral

Given: we have an integral

Explanation: we have

let us consider

so the integral becomes

Step 2

now putting the value of t then we have