Math, asked by vatsal678a, 11 months ago

integration of cos²x​

Answers

Answered by brunoconti
5

Answer:

Step-by-step explanation:

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

Attachments:
Answered by harendrachoubay
14

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.

Similar questions