What is the integral from 0 to t of cos(wt) ?

The integral from 0 to t of cos(wt) is (sin(wt))/w

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to t of cos(wt)

\int_{0}^{t} cos (wt) d t

\frac{sin ( wt )}{w}

Solution steps

\int_{0}^{t} cos (wt) d t

Apply u-substitution

: \int_{0}^{wt} \frac{cos ( u )}{w} d u

= \int_{0}^{wt} \frac{cos ( u )}{w} d u

Take the constant out:

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

= \frac{1}{w} \cdot \int_{0}^{wt} cos (u) d u

Use the common integral:

\int cos (u) d u = sin (u)

= \frac{1}{w} [sin (u)]_{0}^{wt}

Compute the boundaries:

sin (wt)

= \frac{1}{w} sin (wt)

Simplify

= \frac{sin ( wt )}{w}

\int_{0}^{1} 1 + e^{x} d x

\int_{- 2}^{2} 5 x^{4} d x

\int_{0}^{1} 2 x (e^{x^{2}} - 1) d x

\int_{- 1}^{3} \frac{1}{x ^{4}} d x

What is the integral from 0 to t of cos(wt) ?
The integral from 0 to t of cos(wt) is (sin(wt))/w