What is the integral from 0 to y of sin(x+y) ?

The integral from 0 to y of sin(x+y) is -cos(2y)+cos(y)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to y of sin(x+y)

\int_{0}^{y} sin (x + y) d x

- cos (2 y) + cos (y)

Solution steps

\int_{0}^{y} sin (x + y) d x

Apply u-substitution

: \int_{y}^{2 y} sin (u) d u

= \int_{y}^{2 y} sin (u) d u

Use the common integral:

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

= [- cos (u)]_{y}^{2 y}

Compute the boundaries:

- cos (2 y) + cos (y)

= - cos (2 y) + cos (y)

\int_{3}^{6} \frac{1}{x ^{2} - 4} d x

\int_{2}^{9} x d x

\int_{0}^{18} 124 - 6 x d x

\int_{1}^{2} x 1 + x^{2} d x

\int_{0}^{3} 4 - t d t

What is the integral from 0 to y of sin(x+y) ?
The integral from 0 to y of sin(x+y) is -cos(2y)+cos(y)