What is the integral from 0 to pi/(12) of cos(3x) ?

The integral from 0 to pi/(12) of cos(3x) is 1/(3sqrt(2))

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integral from 0 to pi/(12) of cos(3x)

\int_{0}^{\frac{π}{12}} cos (3 x) d x

\frac{1}{3 2}

Decimal Notation

0.23570 \dots

Solution steps

\int_{0}^{\frac{π}{12}} cos (3 x) d x

Apply u-substitution

: \int_{0}^{\frac{π}{4}} cos (u) \frac{1}{3} d u

= \int_{0}^{\frac{π}{4}} cos (u) \frac{1}{3} d u

Take the constant out:

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

= \frac{1}{3} \cdot \int_{0}^{\frac{π}{4}} cos (u) d u

Use the common integral:

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

= \frac{1}{3} [sin (u)]_{0}^{\frac{π}{4}}

Compute the boundaries:

\frac{1}{2}

= \frac{1}{3} \cdot \frac{1}{2}

Simplify

= \frac{1}{3 2}

f (x) = 9 x + 4

x - 6, x^{2} - 12

9 e^{- 3 x}

\int x^{2} 4 + x^{3} d x

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

What is the integral from 0 to pi/(12) of cos(3x) ?
The integral from 0 to pi/(12) of cos(3x) is 1/(3sqrt(2))