What is the integral from 0 to pi/(54) of cos(9x) ?

The integral from 0 to pi/(54) of cos(9x) is 1/18

Popular >

integral from 0 to pi/(54) of cos(9x)

\int_{0}^{\frac{π}{54}} cos (9 x) d x

\frac{1}{18}

Decimal

0.05555 \dots

Solution steps

\int_{0}^{\frac{π}{54}} cos (9 x) d x

Apply u-substitution

: \int_{0}^{\frac{π}{6}} cos (u) \frac{1}{9} d u

= \int_{0}^{\frac{π}{6}} cos (u) \frac{1}{9} d u

Take the constant out:

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

= \frac{1}{9} \cdot \int_{0}^{\frac{π}{6}} cos (u) d u

Use the common integral:

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

= \frac{1}{9} [sin (u)]_{0}^{\frac{π}{6}}

Compute the boundaries:

\frac{1}{2}

= \frac{1}{9} \cdot \frac{1}{2}

Simplify

= \frac{1}{18}

\int_{0}^{3} (x^{2} - 4) d x

\int_{0}^{1} \frac{1}{x ^{\frac{5}{3}}} d x

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

\int_{0}^{4} e^{- x^{2}} d x

\int_{- 1}^{0} (1 + x) d x

What is the integral from 0 to pi/(54) of cos(9x) ?
The integral from 0 to pi/(54) of cos(9x) is 1/18