What is the integral from 0 to pi of cos(2x) ?

The integral from 0 to pi of cos(2x) is 0

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integral from 0 to pi of cos(2x)

\int_{0}^{π} cos (2 x) d x

0

Solution steps

\int_{0}^{π} cos (2 x) d x

Apply u-substitution

: \int_{0}^{2 π} cos (u) \frac{1}{2} d u

= \int_{0}^{2 π} cos (u) \frac{1}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int_{0}^{2 π} cos (u) d u

Use the common integral:

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

= \frac{1}{2} [sin (u)]_{0}^{2 π}

Compute the boundaries:

0

= \frac{1}{2} \cdot 0

Simplify

= 0

\int \frac{x}{x ^{2} - 3} d x

\frac{1}{x ( x ^{2} + 2 x + x )}

f (x) = 3 ln (x)

\frac{d}{d x} (\frac{1}{6 x + 5})

\frac{\partial}{\partial y} (7 ln (2 x^{5} - 3 y))

What is the integral from 0 to pi of cos(2x) ?
The integral from 0 to pi of cos(2x) is 0