Question

integration of cos²x​

Answer 1

Answer:

Step-by-step explanation:

brainliest brainliest brainliest brainliest brainliest brainliest brainliest brainliest brainliest brainliest brainliest brainliest

Answer 2

The integration of $\cos^{2}x$ is $\frac{1}{2}x+ {\frac{\sin 2x}{4} } +c.$

Step-by-step explanation:

Let I =$\int {\cos^{2}x } \, dx$         .

To find, $\int {\cos^{2}x } \, dx$= ?

We know that,

$\cos^{2} x=\frac{1+\cos 2x}{2}$

Now, equation (1) can be written as,

$I =\int {\frac{1+\cos 2x}{2}} \, dx$

$I =\int {\frac{1}{2} } \, dx +\int {\frac{\cos 2x}{2} } \, dx$

$I = \frac{1}{2}x+ \frac{1}{2} {\frac{\sin 2x}{2} } +c$

[∵ $\int {\cos x} \, dx = \cos x$

where, c is called integration constant.

$I = \frac{1}{2}x+{\frac{\sin 2x}{4} } +c$

Hence, the integration of $\cos^{2}x$ is $\frac{1}{2}x+ {\frac{\sin 2x}{4} } +c$.