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

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

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

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

- 2

Solution steps

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

Take the constant out:

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

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

Use the common integral:

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

= 2 [- cos (x)]_{\frac{π}{2}}^{2 π}

Compute the boundaries:

- 1

= 2 (- 1)

Simplify

= - 2

\int_{- 7}^{7} ∣ 6 x ∣ - (x^{2} - 7) d x

\int_{0}^{1} π (- x^{2} + 1)^{2} d x

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

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

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

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