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

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}

in v erse l a pl a ce \frac{- 3}{( s - 1 ) ^{2}}

d er i v a t i v e f (x) = \frac{x ^{3}}{3} + 4 x^{2} + 12 x + 19

e^{x} (y - 1) d x + 2 (e^{x} + 4) d y = 0

d er i v a t i v e \frac{3}{x ^{4} + 7 x + 1}

x \to 1 lim ([2 f (x) + g (x)])

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