What is the integral of sin(x)sin(x) ?

The integral of sin(x)sin(x) is 1/2 (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 sin(x)sin(x)

\int sin (x) sin (x) d x

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

Solution steps

\int sin (x) sin (x) d x

Simplify

sin (x) sin (x) : sin^{2} (x)

= \int sin^{2} (x) d x

Rewrite using trig identities

= \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

= \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

= \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)

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

Add a constant to the solution

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

y = ln (x^{2}), at x = 4

\frac{\partial}{\partial y} (\frac{1}{x y ^{2} - x ^{2} y})

\int \frac{x}{3 + x ^{2}} d x

x y^{^{'}} - 2 y = x^{3}

y = x - 1, y = 0, x = 9

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