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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from 0 to cos(x) of ysin(x)

\int_{0}^{c o s (x)} y sin (x) d y

\frac{cos ^{2} ( x ) sin ( x )}{2}

Solution steps

\int_{0}^{c o s (x)} y sin (x) d y

Take the constant out:

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

= sin (x) \cdot \int_{0}^{c o s (x)} y d y

Apply the Power Rule

= sin (x) [\frac{y ^{2}}{2}]_{0}^{c o s (x)}

Compute the boundaries:

\frac{cos ^{2} ( x )}{2}

= sin (x) \frac{cos ^{2} ( x )}{2}

Simplify

= \frac{cos ^{2} ( x ) sin ( x )}{2}

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