What is the integral from 5 to x of sqrt(p^2)sin(p) ?

The integral from 5 to x of sqrt(p^2)sin(p) is -xcos(x)+sin(x)+5cos(5)-sin(5)

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integral from 5 to x of sqrt(p^2)sin(p)

\int_{5}^{x} p^{2} sin (p) d p

- x cos (x) + sin (x) + 5 cos (5) - sin (5)

Solution steps

\int_{5}^{x} p^{2} sin (p) d p

p^{2} = (p),

assuming

p \geq 0

= \int_{5}^{x} p sin (p) d p

Apply Integration By Parts

= [- p cos (p) - \int - cos (p) d p]_{5}^{x}

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

= [- p cos (p) - (- sin (p))]_{5}^{x}

Simplify

= [- p cos (p) + sin (p)]_{5}^{x}

Compute the boundaries:

- x cos (x) + sin (x) + 5 cos (5) - sin (5)

= - x cos (x) + sin (x) + 5 cos (5) - sin (5)

What is the integral from 5 to x of sqrt(p^2)sin(p) ?
The integral from 5 to x of sqrt(p^2)sin(p) is -xcos(x)+sin(x)+5cos(5)-sin(5)