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

The integral from 0 to pi of cos(θ/2) 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 of cos(θ/2)

\int_{0}^{π} cos (\frac{θ}{2}) d θ

2

Solution steps

\int_{0}^{π} cos (\frac{θ}{2}) d θ

Apply u-substitution

: \int_{0}^{\frac{π}{2}} cos (u) \cdot 2 d u

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

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}} cos (u) d u

Use the common integral:

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

= 2 [sin (u)]_{0}^{\frac{π}{2}}

Compute the boundaries:

1

= 2 \cdot 1

Simplify

= 2

\int_{- 2}^{2} 6 x d x

\int_{0}^{\frac{π}{4}} sin^{5} (2 y) d y

\int_{0}^{2 π} 3 d t

\int_{0}^{\infty} \frac{1}{x ( x ^{2} + 1 )} d x

\int_{1}^{5} x^{2} - 6 x + 5 d x

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