What is the integral from 0 to x of cos(3t) ?

The integral from 0 to x of cos(3t) is 1/3 sin(3x)

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integral from 0 to x of cos(3t)

\int_{0}^{x} cos (3 t) d t

\frac{1}{3} sin (3 x)

Solution steps

\int_{0}^{x} cos (3 t) d t

Apply u-substitution

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

= \int_{0}^{3 x} 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}^{3 x} cos (u) d u

Use the common integral:

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

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

Compute the boundaries:

sin (3 x)

= \frac{1}{3} sin (3 x)

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What is the integral from 0 to x of cos(3t) ?
The integral from 0 to x of cos(3t) is 1/3 sin(3x)