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

The integral of 2cos^2(t) is 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 2cos^2(t)

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

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

Solution steps

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

Take the constant out:

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

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

Rewrite using trig identities

= 2 \cdot \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

= 2 \cdot \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

= 2 \cdot \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)

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

Simplify

2 \cdot \frac{1}{2} (t + \frac{1}{2} sin (2 t)) : t + \frac{1}{2} sin (2 t)

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

Add a constant to the solution

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

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

\int \frac{2}{4 - 2 x} d x

\int \frac{1}{π} x sin (x) d x

\int \frac{x}{2} - \frac{2}{x} d x

\int x (9 x^{2} - 5)^{\frac{3}{2}} d x

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