What is the integral of-sin^2(x) ?

The integral of-sin^2(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^2(x)

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

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

Solution steps

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

Take the constant out:

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

\frac{d}{d x} (\frac{3 x ^{2} - 3}{- 2 x})

\frac{\partial}{\partial x} (8 x^{2})

3 y^{^{''}} - 5 y^{^{'}} - 2 y = x^{3} - 2 x

x \to - 2 lim (x^{3} - 2 x^{2} + 1)

\frac{d}{d x} (arctan (x - 5))

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