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

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

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integral from 0 to pi/2 of xsin(x)

\int_{0}^{\frac{π}{2}} x sin (x) d x

1

Solution steps

\int_{0}^{\frac{π}{2}} x sin (x) d x

Apply Integration By Parts

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

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

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

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

Simplify

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

Compute the boundaries:

1

= 1

x \to 1 lim (+ f (x))

\int_{0}^{1} 4 - y - 2 y - 1 d y

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

x^{2} (\frac{d y}{d x}) - 2 x y = 3 y^{4}

\frac{d}{d x} (3 + x)

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