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

The integral from pi/2 to pi of cos(2x) is 0

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

\int_{\frac{π}{2}}^{π} cos (2 x) d x

0

Solution steps

\int_{\frac{π}{2}}^{π} cos (2 x) d x

Apply u-substitution

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

= \int_{π}^{2 π} cos (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} cos (u) d u

Use the common integral:

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

= \frac{1}{2} [sin (u)]_{π}^{2 π}

Compute the boundaries:

0

= \frac{1}{2} \cdot 0

Simplify

= 0

\int_{0}^{π} (1 + cos (x))^{2} d x

\int_{0}^{π} x sin (\frac{n x}{2}) d x

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

\int_{0}^{1} x^{2} cos (nπ x) d x

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

What is the integral from pi/2 to pi of cos(2x) ?
The integral from pi/2 to pi of cos(2x) is 0