What is the integral from 0 to pi/2 of 4sin(2θ) ?

The integral from 0 to pi/2 of 4sin(2θ) is 4

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 4sin(2θ)

\int_{0}^{\frac{π}{2}} 4 sin (2 θ) d θ

4

Solution steps

\int_{0}^{\frac{π}{2}} 4 sin (2 θ) d θ

Take the constant out:

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

= 4 \cdot \int_{0}^{\frac{π}{2}} sin (2 θ) d θ

Apply u-substitution

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

= 4 \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

= 4 \cdot \frac{1}{2} \cdot \int_{0}^{π} sin (u) d u

Use the common integral:

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

= 4 \cdot \frac{1}{2} [- cos (u)]_{0}^{π}

Simplify

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

= 2 [- cos (u)]_{0}^{π}

Compute the boundaries:

2

= 2 \cdot 2

Simplify

= 4

\int_{0}^{1} (1 + 8 x^{5}) d x

\int_{0}^{1} x (6 x - 6 x^{2}) d x

\int_{3}^{9} (3 - x) (x - 9) d x

\int_{0}^{10} (100 - x^{2}) d x

\int_{0}^{1} x - \frac{x ^{2}}{4} d x

What is the integral from 0 to pi/2 of 4sin(2θ) ?
The integral from 0 to pi/2 of 4sin(2θ) is 4