What is the integral from-pi to 0 of-picos(nx) ?

The integral from-pi to 0 of-picos(nx) is 0

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from-pi to 0 of-picos(nx)

\int_{- π}^{0} - π cos (n x) d x

0

Solution steps

\int_{- π}^{0} - π cos (n x) d x

Take the constant out:

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

= - π \cdot \int_{- π}^{0} cos (n x) d x

Apply u-substitution

: \int_{- πn}^{0} \frac{cos ( u )}{n} d u

= - π \cdot \int_{- πn}^{0} \frac{cos ( u )}{n} d u

Take the constant out:

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

= - π \frac{1}{n} \cdot \int_{- πn}^{0} cos (u) d u

Use the common integral:

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

= - π \frac{1}{n} [sin (u)]_{- πn}^{0}

Simplify

- π \frac{1}{n} [sin (u)]_{- πn}^{0} : - \frac{π}{n} [sin (u)]_{- πn}^{0}

= - \frac{π}{n} [sin (u)]_{- πn}^{0}

Compute the boundaries:

0

= - \frac{π}{n} \cdot 0

Simplify

= 0

\int_{0}^{π} 1 - cos (θ) d θ

\int_{- \frac{π}{4}}^{\frac{π}{2}} cos (x) d x

\int_{- 1}^{1} 9 d x

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

\int_{0}^{8} x 8 - x d x

What is the integral from-pi to 0 of-picos(nx) ?
The integral from-pi to 0 of-picos(nx) is 0