What is the integral from (3pi)/2 to pi of xcos(x) ?

The integral from (3pi)/2 to pi of xcos(x) is (3pi)/2-1

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integral from (3pi)/2 to pi of xcos(x)

\int_{\frac{3 π}{2}}^{π} x cos (x) d x

\frac{3 π}{2} - 1

Decimal

3.71238 \dots

Solution steps

\int_{\frac{3 π}{2}}^{π} x cos (x) d x

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{π}^{\frac{3 π}{2}} x cos (x) d x

Apply Integration By Parts

: [x sin (x) - \int sin (x) d x]_{π}^{\frac{3 π}{2}}

= - [x sin (x) - \int sin (x) d x]_{π}^{\frac{3 π}{2}}

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

= - [x sin (x) - (- cos (x))]_{π}^{\frac{3 π}{2}}

Simplify

= - [x sin (x) + cos (x)]_{π}^{\frac{3 π}{2}}

Compute the boundaries:

- \frac{3 π}{2} + 1

= - (- \frac{3 π}{2} + 1)

Simplify

= \frac{3 π}{2} - 1

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What is the integral from (3pi)/2 to pi of xcos(x) ?
The integral from (3pi)/2 to pi of xcos(x) is (3pi)/2-1