What is the integral from 0 to t of cos(2wt) ?

The integral from 0 to t of cos(2wt) is (sin(2wt))/(2w)

Popular >

integral from 0 to t of cos(2wt)

\int_{0}^{t} cos (2 wt) d t

\frac{sin ( 2 wt )}{2 w}

Solution steps

\int_{0}^{t} cos (2 wt) d t

Apply u-substitution

: \int_{0}^{2 wt} \frac{cos ( u )}{2 w} d u

= \int_{0}^{2 wt} \frac{cos ( u )}{2 w} d u

Take the constant out:

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

= \frac{1}{2 w} \cdot \int_{0}^{2 wt} cos (u) d u

Use the common integral:

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

= \frac{1}{2 w} [sin (u)]_{0}^{2 wt}

Compute the boundaries:

sin (2 wt)

= \frac{1}{2 w} sin (2 wt)

Simplify

= \frac{sin ( 2 wt )}{2 w}

\int_{3}^{9} 2 x - 2 - x + 5 d x

\int_{- 1}^{2} (2 x^{3} + x^{2} - 8) d x

\int_{\frac{π}{2}}^{π} 2 sin^{2} (θ) d θ

\int_{0}^{4} y e^{y^{2}} d y

\int_{0}^{x} e^{- 5 t^{4}} d t

What is the integral from 0 to t of cos(2wt) ?
The integral from 0 to t of cos(2wt) is (sin(2wt))/(2w)