What is the integral of sin(2x-pi/2) ?

The integral of sin(2x-pi/2) is -1/2 sin(2x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of sin(2x-pi/2)

\int sin (2 x - \frac{π}{2}) d x

- \frac{1}{2} sin (2 x) + C

Solution steps

\int sin (2 x - \frac{π}{2}) d x

Rewrite using trig identities

= \int - cos (2 x) d x

Take the constant out:

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

= - \int cos (2 x) d x

Apply u-substitution

: \int cos (u) \frac{1}{2} d u

= - \int cos (u) \frac{1}{2} d u

Take the constant out:

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

= - \frac{1}{2} \cdot \int cos (u) d u

Use the common integral:

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

= - \frac{1}{2} sin (u)

Substitute back

u = 2 x

= - \frac{1}{2} sin (2 x)

Add a constant to the solution

= - \frac{1}{2} sin (2 x) + C

\int (a^{2} - x^{2})^{\frac{3}{2}} d x

lo g_{5} (x^{2} - 4)

\frac{d}{d θ} (5 sin (2 θ))

y^{^{''}} + 3 y = 0

\int \frac{x ^{2} + 2 x + 3}{x ^{3} - x} d x

What is the integral of sin(2x-pi/2) ?
The integral of sin(2x-pi/2) is -1/2 sin(2x)+C