What is the integral of cos(2-x) ?

The integral of cos(2-x) is sin(x-2)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of cos(2-x)

\int cos (2 - x) d x

sin (x - 2) + C

Solution steps

\int cos (2 - x) d x

Rewrite using trig identities

= \int cos (2) cos (x) + sin (2) sin (x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int cos (2) cos (x) d x + \int sin (2) sin (x) d x

\int cos (2) cos (x) d x = cos (2) sin (x)

\int sin (2) sin (x) d x = - sin (2) cos (x)

= cos (2) sin (x) - sin (2) cos (x)

Use the Angle Difference identity:

sin (s) cos (t) - cos (s) sin (t) = sin (s - t)

= sin (x - 2)

Add a constant to the solution

= sin (x - 2) + C

\int \frac{e ^{\frac{y}{x}}}{x} d x

\int \frac{e ^{l n (x)}}{x ^{2} + 4} d x

\int \frac{x ^{\frac{- 1}{3}} - 5}{x} d x

\int \frac{2 x + 1}{x ^{2} - 2 x + 2} d x