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

The integral from 0 to x of cos(2x) is 1/2 sin(2x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to x of cos(2x)

\int_{0}^{x} cos (2 x) d x

\frac{1}{2} sin (2 x)

Solution steps

\int_{0}^{x} cos (2 x) d x

Apply u-substitution

: \int_{0}^{2 x} cos (u) \frac{1}{2} d u

= \int_{0}^{2 x} cos (u) \frac{1}{2} d u

Take the constant out:

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

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

Use the common integral:

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

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

Compute the boundaries:

sin (2 x)

= \frac{1}{2} sin (2 x)

\int_{0}^{\infty} e^{- s t} 1 d t

\int_{2}^{5} ∣ x - 4 ∣ d x

\int_{0}^{2} 5 x (x - 7) d x

\int_{- 2}^{2} (1 - ∣ x ∣^{3}) d x

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

What is the integral from 0 to x of cos(2x) ?
The integral from 0 to x of cos(2x) is 1/2 sin(2x)