Check the solution to "Solve the following indefinite integrals. ∫(cos⁡x2−sin⁡x2)2dx"

Ava-May Nelson

Answered question

2021-09-21

Solve the following indefinite integrals.

\int {(\cos \frac{x}{2} - \sin \frac{x}{2})}^{2} d x

likvau

Skilled2021-09-22Added 75 answers

To find:
The indefinite integral of

\int {(\cos (\frac{x}{2}) - \sin (\frac{x}{2}))}^{2} d x

.
Calculation:
The indefinite integral of

\int {(\cos (\frac{x}{2}) - \sin (\frac{x}{2}))}^{2} d x

can be obtained as,

\int {(\cos (\frac{x}{2}) - \sin (\frac{x}{2}))}^{2} d x = \int \sin^{2} (\frac{x}{2}) + \cos^{2} (\frac{x}{2}) - 2 \sin (\frac{x}{2}) \cos (\frac{x}{2}) d x

= \int 1 - \sin x d x

= x + \cos x + C

Thus, the integral of

\int {(\cos (\frac{x}{2}) - \sin (\frac{x}{2}))}^{2} d x i s x + \cos x + C

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?