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

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

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integral from 0 to pi/4 of (sin(4x))

\int_{0}^{\frac{π}{4}} (sin (4 x)) d x

\frac{1}{2}

Decimal

0.5

Solution steps

\int_{0}^{\frac{π}{4}} sin (4 x) d x

Apply u-substitution

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

Take the constant out:

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

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

Use the common integral:

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

= \frac{1}{4} [- cos (u)]_{0}^{π}

Compute the boundaries:

2

= \frac{1}{4} \cdot 2

Simplify

= \frac{1}{2}

a re a x^{3} - 12 x^{2} + 20 x, - x^{3} + 12 x^{2} - 20 x

f (x) = 7 tan (x)

t an g e n t 7 x

\int x^{5} e^{x} d x

\frac{d}{d x} (1 x^{2})

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