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

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

Popular >

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

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

\frac{1}{2} - \frac{π}{4 2}

Decimal Notation

0.15174 \dots

Solution steps

\int_{0}^{\frac{π}{4}} x sin (x) d x

Apply Integration By Parts

: [- x cos (x) - \int - cos (x) d x]_{0}^{\frac{π}{4}}

= [- x cos (x) - \int - cos (x) d x]_{0}^{\frac{π}{4}}

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

= [- x cos (x) - (- sin (x))]_{0}^{\frac{π}{4}}

Simplify

= [- x cos (x) + sin (x)]_{0}^{\frac{π}{4}}

Compute the boundaries:

\frac{1}{2} - \frac{π}{4 2}

= \frac{1}{2} - \frac{π}{4 2}

\int_{0}^{10} \frac{1}{10 - x} d x

\int_{0}^{1} t (1 + i t^{2})^{3} d t

\int_{1}^{4} (x - 2)^{2} - x d x

\int_{0}^{3} (\frac{x}{1 + x ^{4}}) d x

\int_{- 1}^{1} 2 x^{3} + \frac{3 ^{x}}{2} d x

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