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

The integral from pi/4 to pi of sin(2x) is -1/2

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integral from pi/4 to pi of sin(2x)

\int_{\frac{π}{4}}^{π} sin (2 x) d x

- \frac{1}{2}

Decimal Notation

- 0.5

Solution steps

\int_{\frac{π}{4}}^{π} sin (2 x) d x

Apply u-substitution

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

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

Use the common integral:

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

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

Compute the boundaries:

- 1

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

Simplify

= - \frac{1}{2}

e^{\frac{7}{x}}

n = 0 \sum \infty ln (\frac{1}{n + 1})

\frac{d y}{d x} = \frac{2 x y - y ^{2}}{2 x y - x ^{2}}

y = 8 x sin (x)

x \to 0 lim (\frac{sin ( 3 ) ( x )}{x})

What is the integral from pi/4 to pi of sin(2x) ?
The integral from pi/4 to pi of sin(2x) is -1/2