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

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

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

\int_{0}^{\frac{π}{2}} cos (x) x d x

\frac{π}{2} - 1

Decimal

0.57079 \dots

Solution steps

\int_{0}^{\frac{π}{2}} cos (x) x d x

Apply Integration By Parts

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

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

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

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

Simplify

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

Compute the boundaries:

\frac{π}{2} - 1

= \frac{π}{2} - 1

\int_{0}^{2} π (x^{4} - 4 x^{2}) d x

\int_{1}^{2} 2 x - 1 d x

\int_{0}^{1} 9 x^{3} d x

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

\int_{2}^{3} - \frac{4}{x ^{2}} d x

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