What is the integral from 0 to x/2 of xcos(x) ?

The integral from 0 to x/2 of xcos(x) is (xsin(x/2))/2+cos(x/2)-1

Popular >

integral from 0 to x/2 of xcos(x)

\int_{0}^{\frac{x}{2}} x cos (x) d x

\frac{x sin ( \frac{x}{2} )}{2} + cos (\frac{x}{2}) - 1

Solution steps

\int_{0}^{\frac{x}{2}} x cos (x) d x

Apply Integration By Parts

: [x sin (x) - \int sin (x) d x]_{0}^{\frac{x}{2}}

= [x sin (x) - \int sin (x) d x]_{0}^{\frac{x}{2}}

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

= [x sin (x) - (- cos (x))]_{0}^{\frac{x}{2}}

Simplify

= [x sin (x) + cos (x)]_{0}^{\frac{x}{2}}

Compute the boundaries:

\frac{1}{2} x sin (\frac{x}{2}) + cos (\frac{x}{2}) - 1

= \frac{1}{2} x sin (\frac{x}{2}) + cos (\frac{x}{2}) - 1

Simplify

= \frac{x sin ( \frac{x}{2} )}{2} + cos (\frac{x}{2}) - 1

\int_{0}^{1} 3 x^{2} (1 - x)^{2} d x

\int_{0}^{2} (2 x - 3) (8 x^{2} + 6) d x

\int_{0}^{2} t e^{- t^{2}} d t

\int_{0}^{3} x^{2} \cdot e^{x} d x

\int_{3}^{x^{4}} sin (5 t) t^{5} d t

What is the integral from 0 to x/2 of xcos(x) ?
The integral from 0 to x/2 of xcos(x) is (xsin(x/2))/2+cos(x/2)-1