What is the integral from 0 to kpi of xsin(x) ?

The integral from 0 to kpi of xsin(x) is sin(pik)-pikcos(pik)

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integral from 0 to kpi of xsin(x)

\int_{0}^{kπ} x sin (x) d x

sin (πk) - πk cos (πk)

Solution steps

\int_{0}^{kπ} x sin (x) d x

Apply Integration By Parts

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

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

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

= [- x cos (x) - (- sin (x))]_{0}^{πk}

Simplify

= [- x cos (x) + sin (x)]_{0}^{πk}

Compute the boundaries:

sin (πk) - πk cos (πk)

= sin (πk) - πk cos (πk)

\int_{1}^{2} \frac{1}{2} - \frac{1}{8} x d x

\int_{2}^{4} 3 ln (x) d x

\int_{1}^{3} x^{3} - 2 x^{2} - 5 x + 6 d x

\int_{\frac{y ^{2}}{4}}^{\frac{y + 4}{2}} 2 y d y

\int_{- 5}^{3} (- x^{2} - 2 x + 15) d x

What is the integral from 0 to kpi of xsin(x) ?
The integral from 0 to kpi of xsin(x) is sin(pik)-pikcos(pik)