What is the integral from 0 to pi of sin(5x) ?

The integral from 0 to pi of sin(5x) is 2/5

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integral from 0 to pi of sin(5x)

\int_{0}^{π} sin (5 x) d x

\frac{2}{5}

Decimal

0.4

Solution steps

\int_{0}^{π} sin (5 x) d x

Apply u-substitution

= \int_{0}^{5 π} sin (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}^{5 π} sin (u) d u

Use the common integral:

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

= \frac{1}{5} [- cos (u)]_{0}^{5 π}

Compute the boundaries:

2

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

Simplify

= \frac{2}{5}

t an g e n t 5 x - 2 x^{2}

\frac{d}{d x} (e^{e x})

\int \frac{4 - x}{16 - x ^{2}} d x

d er i v a t i v e f (x) = 5 (9 x^{7} + 3 x^{4} - 2)^{3}

x \to 0 + lim (x^{\frac{4}{x}})

What is the integral from 0 to pi of sin(5x) ?
The integral from 0 to pi of sin(5x) is 2/5