What is the integral from 0 to pi/(20) of cos(5x) ?

The integral from 0 to pi/(20) of cos(5x) is 1/(5sqrt(2))

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integral from 0 to pi/(20) of cos(5x)

\int_{0}^{\frac{π}{20}} cos (5 x) d x

\frac{1}{5 2}

Decimal Notation

0.14142 \dots

Solution steps

\int_{0}^{\frac{π}{20}} cos (5 x) d x

Apply u-substitution

: \int_{0}^{\frac{π}{4}} cos (u) \frac{1}{5} d u

= \int_{0}^{\frac{π}{4}} cos (u) \frac{1}{5} d u

Take the constant out:

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

= \frac{1}{5} \cdot \int_{0}^{\frac{π}{4}} cos (u) d u

Use the common integral:

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

= \frac{1}{5} [sin (u)]_{0}^{\frac{π}{4}}

Compute the boundaries:

\frac{1}{2}

= \frac{1}{5} \cdot \frac{1}{2}

Simplify

= \frac{1}{5 2}

x \to 0 + lim (\frac{7}{x ^{3} + 2 x ^{2}})

\frac{d}{d x} (e^{2 x + l n (x)})

\frac{x ^{2} - x - 2}{x ^{2} + x - 6}

y^{^{''}} - 8 y^{^{'}} + 9 y = 0

x \to 4 lim (\frac{x ^{2} - 4}{x - 4})

What is the integral from 0 to pi/(20) of cos(5x) ?
The integral from 0 to pi/(20) of cos(5x) is 1/(5sqrt(2))