What is the integral from 0 to 4 of ycos(y) ?

The integral from 0 to 4 of ycos(y) is 4sin(4)+cos(4)-1

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integral from 0 to 4 of ycos(y)

\int_{0}^{4} y cos (y) d y

4 sin (4) + cos (4) - 1

Decimal Notation

- 4.68085 \dots

Solution steps

\int_{0}^{4} y cos (y) d y

Apply Integration By Parts

: [y sin (y) - \int sin (y) d y]_{0}^{4}

= [y sin (y) - \int sin (y) d y]_{0}^{4}

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

= [y sin (y) - (- cos (y))]_{0}^{4}

Simplify

= [y sin (y) + cos (y)]_{0}^{4}

Compute the boundaries:

4 sin (4) + cos (4) - 1

= 4 sin (4) + cos (4) - 1

\int_{2}^{4} x + 5 x^{2} d x

\int_{1}^{e} x ln (x^{2}) d x

\int_{1}^{2} \frac{1}{x ( x ^{2} + 1 )} d x

\int_{0}^{1.5} e^{- x} cos (x) d x

\int_{- 2}^{2} x^{2} (4 - x^{2}) d x

What is the integral from 0 to 4 of ycos(y) ?
The integral from 0 to 4 of ycos(y) is 4sin(4)+cos(4)-1