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

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

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

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

- π

Decimal Notation

- 3.14159 \dots

Solution steps

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

Take the constant out:

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

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

Use the common integral:

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

= \frac{π}{2} [- cos (x)]_{π}^{2 π}

Compute the boundaries:

- 2

= \frac{π}{2} (- 2)

Simplify

= - π

\int_{1}^{\infty} \frac{x}{2 ^{x}} d x

\int_{1}^{3} x^{2} + 1 d x

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

\int_{2}^{3} (2 x - x^{2}) d x

\int_{t}^{0} e^{a x} d x

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