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

The integral from pi/2 to pi of sin(2x) is -1

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

\int_{\frac{π}{2}}^{π} sin (2 x) d x

- 1

Solution steps

\int_{\frac{π}{2}}^{π} sin (2 x) d x

Apply u-substitution

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

= \int_{π}^{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_{π}^{2 π} sin (u) d u

Use the common integral:

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

= \frac{1}{2} [- cos (u)]_{π}^{2 π}

Compute the boundaries:

- 2

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

Simplify

= - 1

\frac{sin ( x ) - x}{x ^{2}}

x \to 0 lim (sin (\frac{1}{∣ x ∣}))

\frac{3 x ^{2}}{4}

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

\frac{\partial}{\partial x} (3 x^{2} + 2 y)

What is the integral from pi/2 to pi of sin(2x) ?
The integral from pi/2 to pi of sin(2x) is -1