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

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

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integral from pi to 2pi of sin(2x)

\int_{π}^{2 π} sin (2 x) d x

0

Solution steps

\int_{π}^{2 π} sin (2 x) d x

Apply u-substitution

: \int_{2 π}^{4 π} sin (u) \frac{1}{2} d u

= \int_{2 π}^{4 π} sin (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_{2 π}^{4 π} sin (u) d u

Use the common integral:

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

= \frac{1}{2} [- cos (u)]_{2 π}^{4 π}

Compute the boundaries:

0

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

Simplify

= 0

\int_{0}^{4} \frac{1}{2 + x} d x

\int_{- π}^{0} - cos (x) d x

\int_{0}^{\frac{1}{2}} (2 x + 1)^{- 2} d x

\int_{0}^{1} (2 x - 1)^{4} d x

\int_{0}^{1} 100 e^{- 0.01 x} d x

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