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

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

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

\int_{0}^{\frac{π}{2}} cos (2 x) d x

0

Solution steps

\int_{0}^{\frac{π}{2}} cos (2 x) d x

Apply u-substitution

: \int_{0}^{π} cos (u) \frac{1}{2} d u

= \int_{0}^{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_{0}^{π} cos (u) d u

Use the common integral:

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

= \frac{1}{2} [sin (u)]_{0}^{π}

Compute the boundaries:

0

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

Simplify

= 0

\frac{d}{d x} (\frac{1}{4} cos (\frac{x}{4}))

- x + 2

\int \frac{e ^{x}}{1 - 9 e ^{2 x}} d x

\int \frac{1}{4 x ^{2} + 7} d x

(x, y) \to (0, 0) lim (\frac{2 x}{x ^{2} + x + y ^{2}})

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