What is the integral from pi/3 to pi of sin(2x) ?

The integral from pi/3 to pi of sin(2x) is -3/4

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integral from pi/3 to pi of sin(2x)

\int_{\frac{π}{3}}^{π} sin (2 x) d x

- \frac{3}{4}

Decimal

- 0.75

Solution steps

\int_{\frac{π}{3}}^{π} sin (2 x) d x

Apply u-substitution

: \int_{\frac{2 π}{3}}^{2 π} sin (u) \frac{1}{2} d u

= \int_{\frac{2 π}{3}}^{2 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_{\frac{2 π}{3}}^{2 π} sin (u) d u

Use the common integral:

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

= \frac{1}{2} [- cos (u)]_{\frac{2 π}{3}}^{2 π}

Compute the boundaries:

- \frac{3}{2}

= \frac{1}{2} (- \frac{3}{2})

Simplify

= - \frac{3}{4}

\int_{- π}^{0} 6 x^{2} d x

\int_{0}^{1} 6 x^{5} (4 - x^{6}) d x

\int_{- 1}^{1} e^{- 2 x} - 1 d x

\int_{0}^{π} x - sin (x) d x

\int_{0}^{1} \frac{3 x - 2}{x + 2} d x

What is the integral from pi/3 to pi of sin(2x) ?
The integral from pi/3 to pi of sin(2x) is -3/4