What is the integral of pi/2 sin(pi/6 x) ?

The integral of pi/2 sin(pi/6 x) is -3cos(pi/6 x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of pi/2 sin(pi/6 x)

\int \frac{π}{2} sin (\frac{π}{6} x) d x

- 3 cos (\frac{π}{6} x) + C

Solution steps

\int \frac{π}{2} sin (\frac{π}{6} x) d x

Take the constant out:

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

= \frac{π}{2} \cdot \int sin (\frac{π}{6} x) d x

Apply u-substitution

: \int sin (u) \frac{6}{π} d u

= \frac{π}{2} \cdot \int sin (u) \frac{6}{π} d u

Take the constant out:

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

= \frac{π}{2} \cdot \frac{6}{π} \cdot \int sin (u) d u

Use the common integral:

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

= \frac{π}{2} \cdot \frac{6}{π} (- cos (u))

Substitute back

u = \frac{π}{6} x

= \frac{π}{2} \cdot \frac{6}{π} (- cos (\frac{π}{6} x))

Simplify

\frac{π}{2} \cdot \frac{6}{π} (- cos (\frac{π}{6} x)) : - 3 cos (\frac{π}{6} x)

= - 3 cos (\frac{π}{6} x)

Add a constant to the solution

= - 3 cos (\frac{π}{6} x) + C

\int \frac{2 x}{x - 2} d x

\int \frac{1}{81 + 36 x ^{2}} d x

\int \frac{1}{( 1 + 4 x ) ^{2}} d x

\int e^{20} sin (3 θ) d θ

\int 7 sin (2 x) d x

What is the integral of pi/2 sin(pi/6 x) ?
The integral of pi/2 sin(pi/6 x) is -3cos(pi/6 x)+C