What is the integral of-cos^2(t) ?

The integral of-cos^2(t) is -1/2 (t+1/2 sin(2t))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of-cos^2(t)

\int - cos^{2} (t) d t

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

Solution steps

\int - cos^{2} (t) d t

Take the constant out:

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

= - \int cos^{2} (t) d t

Rewrite using trig identities

= - \int \frac{1 + cos ( 2 t )}{2} d t

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 t) d t

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 t + \int cos (2 t) d t)

\int 1 d t = t

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

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

Add a constant to the solution

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

\frac{\partial}{\partial x} (2^{x^{2} - y^{5}})

x^{3} - 8 x^{2} + 5 x - 2

\frac{\partial}{\partial x} (4 e^{x y + 3})

(7 x^{6} + 2 x^{3})^{4}

x + 8

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