What is the integral from 0 to pi/4 of cos(2x) ?

The integral from 0 to pi/4 of cos(2x) is 1/2

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integral from 0 to pi/4 of cos(2x)

\int_{0}^{\frac{π}{4}} cos (2 x) d x

\frac{1}{2}

Decimal Notation

0.5

Solution steps

\int_{0}^{\frac{π}{4}} cos (2 x) d x

Apply u-substitution

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

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

Use the common integral:

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

= \frac{1}{2} [sin (u)]_{0}^{\frac{π}{2}}

Compute the boundaries:

1

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

Simplify

= \frac{1}{2}

y = (3 x^{3} + 7)^{2}

\int (x + 2)^{- 1} d x

\frac{d y}{d x} = 7 x^{2} \cdot \frac{1}{5 y ^{2}}

\frac{d}{d x} (7 x^{\frac{1}{3}})

x \to 2 lim (\frac{2}{x - 2})

What is the integral from 0 to pi/4 of cos(2x) ?
The integral from 0 to pi/4 of cos(2x) is 1/2