What is the integral from-pi to pi of cos(3x) ?

The integral from-pi to pi of cos(3x) is 0

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integral from-pi to pi of cos(3x)

\int_{- π}^{π} cos (3 x) d x

0

Solution steps

\int_{- π}^{π} cos (3 x) d x

Apply u-substitution

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

= \int_{- 3 π}^{3 π} 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_{- 3 π}^{3 π} cos (u) d u

Use the common integral:

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

= \frac{1}{3} [sin (u)]_{- 3 π}^{3 π}

Compute the boundaries:

0

= \frac{1}{3} \cdot 0

Simplify

= 0

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

\frac{d}{d x} (csc (x^{3} + 2 x) - tan (x))

\frac{\partial}{\partial z} (- y^{2} sin (z))

x \to - 1 + lim ((x + 2 x^{3})^{4})

x \to 0 lim (x^{2} + 9 - 3)

What is the integral from-pi to pi of cos(3x) ?
The integral from-pi to pi of cos(3x) is 0