What is the integral of pisin^2(x) ?

The integral of pisin^2(x) is pi/2 (x-1/2 sin(2x))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of pisin^2(x)

\int π sin^{2} (x) d x

\frac{π}{2} (x - \frac{1}{2} sin (2 x)) + C

Solution steps

\int π sin^{2} (x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= π \cdot \int sin^{2} (x) d x

Rewrite using trig identities

= π \cdot \int \frac{1 - cos ( 2 x )}{2} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= π \frac{1}{2} \cdot \int 1 - cos (2 x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= π \frac{1}{2} (\int 1 d x - \int cos (2 x) d x)

\int 1 d x = x

\int cos (2 x) d x = \frac{1}{2} sin (2 x)

= π \frac{1}{2} (x - \frac{1}{2} sin (2 x))

Simplify

π \frac{1}{2} (x - \frac{1}{2} sin (2 x)) : \frac{π}{2} (x - \frac{1}{2} sin (2 x))

= \frac{π}{2} (x - \frac{1}{2} sin (2 x))

Add a constant to the solution

= \frac{π}{2} (x - \frac{1}{2} sin (2 x)) + C

\int x^{4} cos (x^{5} + 4) d x

\int (14 x + 3) 7 x^{2} + 3 x d x

\int (e^{3 x} + 5) d x

\int \frac{1}{2} csc^{2} (x) + \frac{1}{x ^{2}} d x

\int 11 x x^{2} + 7 d x

What is the integral of pisin^2(x) ?
The integral of pisin^2(x) is pi/2 (x-1/2 sin(2x))+C