What is the integral from 0 to pi/2 of (2sin(2x)) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to pi/2 of (2sin(2x))

\int_{0}^{\frac{π}{2}} (2 sin (2 x)) d x

2

Solution steps

\int_{0}^{\frac{π}{2}} 2 sin (2 x) d x

Take the constant out:

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

= 2 \cdot \int_{0}^{\frac{π}{2}} sin (2 x) d x

Apply u-substitution

: \int_{0}^{π} sin (u) \frac{1}{2} d u

= 2 \cdot \int_{0}^{π} sin (u) \frac{1}{2} d u

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_{0}^{π} sin (u) d u

Use the common integral:

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

= 2 \cdot \frac{1}{2} [- cos (u)]_{0}^{π}

Simplify

2 \cdot \frac{1}{2} [- cos (u)]_{0}^{π} : [- cos (u)]_{0}^{π}

= [- cos (u)]_{0}^{π}

Compute the boundaries:

2

= 2

\int_{- 1}^{1} π (x^{2} - 1)^{2} d x

\int_{0}^{π} 3 x^{2} sin (x^{3}) d x

\int_{0}^{\frac{π}{2}} e^{x} + cos (x) d x

\int_{0}^{z} e^{t^{2}} d t

\int_{0}^{2} 2 π (x - 3) x^{2} d x

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