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

The integral from 0 to sqrt(pi of)xsin(x) is sin(sqrt(pi))-sqrt(pi)cos(sqrt(pi))

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integral from 0 to sqrt(pi of)xsin(x)

\int_{0}^{π} x sin (x) d x

sin (π) - π cos (π)

Decimal

1.33474 \dots

Solution steps

\int_{0}^{π} x sin (x) d x

Apply Integration By Parts

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

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

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

= [- x cos (x) - (- sin (x))]_{0}^{π}

Simplify

= [- x cos (x) + sin (x)]_{0}^{π}

Compute the boundaries:

sin (π) - π cos (π)

= sin (π) - π cos (π)

\int_{- 3}^{3} (x - 3) 9 - x^{2} d x

\int_{2 x^{2}}^{1 + x^{2}} x + 2 y d y

\int_{3}^{9} x^{2} d x

\int_{1}^{6} t^{2} - 2 t - 15 d t

\int_{0}^{y} 2 z d z

What is the integral from 0 to sqrt(pi of)xsin(x) ?
The integral from 0 to sqrt(pi of)xsin(x) is sin(sqrt(pi))-sqrt(pi)cos(sqrt(pi))