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

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

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

\int_{0}^{\frac{π}{2}} x \cdot 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

\frac{d}{d x} (cos (2 ln (x)))

\int \frac{10}{r ^{2} + 1} d r

y = 8 - 8 x^{2}, y = 0

6 x^{9} e^{x}

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

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