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Step-by-step Solution

Trigonometric integral $\int_{\frac{\pi }{2}}^{\left(\frac{5\cdot \pi }{2}\right)^2} x\sin\left(x\right)dx$

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Answer

$-27.6188$

Step-by-step explanation

Problem to solve:

$\int_{\frac{\pi }{2}}^{\left(\frac{5\pi }{2}\right)^2} x\cdot\sin\left(x\right)dx$
1

Multiply $5$ times $\pi $

$\int_{\sqrt{2}}^{\left(\frac{15.708}{2}\right)^2} x\sin\left(x\right)dx$
2

Divide $15.708$ by $2$

$\int_{\sqrt{2}}^{7.854^2} x\sin\left(x\right)dx$

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Answer

$-27.6188$
$\int_{\frac{\pi }{2}}^{\left(\frac{5\pi }{2}\right)^2} x\cdot\sin\left(x\right)dx$

Main topic:

Integration by parts

Used formulas:

4. See formulas

Time to solve it:

~ 0.72 seconds