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

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

Popular >

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

\int_{0}^{\frac{π}{4}} sin (2 x) d x

\frac{1}{2}

Decimal Notation

0.5

Solution steps

\int_{0}^{\frac{π}{4}} sin (2 x) d x

Apply u-substitution

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

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

Use the common integral:

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

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

Compute the boundaries:

1

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

Simplify

= \frac{1}{2}

\frac{\partial}{\partial x} (\frac{( 2 x - y )}{x y})

\frac{d}{d x} (a ln (x))

f (x) 0

\frac{- 3 x ^{4} + 1}{( x ^{4} + 1 ) ^{2}}

\int (sec^{3} (3 x)) (tan (3 x)) d x

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