What is the integral from 2 to y of x^2sin(x) ?

The integral from 2 to y of x^2sin(x) is -y^2cos(y)+2ysin(y)+2cos(y)+2cos(2)-4sin(2)

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integral from 2 to y of x^2sin(x)

\int_{2}^{y} x^{2} sin (x) d x

- y^{2} cos (y) + 2 y sin (y) + 2 cos (y) + 2 cos (2) - 4 sin (2)

Solution steps

\int_{2}^{y} x^{2} sin (x) d x

Apply Integration By Parts

: [- x^{2} cos (x) - \int - 2 x cos (x) d x]_{2}^{y}

= [- x^{2} cos (x) - \int - 2 x cos (x) d x]_{2}^{y}

\int - 2 x cos (x) d x = - 2 (x sin (x) + cos (x))

= [- x^{2} cos (x) - (- 2 (x sin (x) + cos (x)))]_{2}^{y}

Simplify

= [- x^{2} cos (x) + 2 (x sin (x) + cos (x))]_{2}^{y}

Compute the boundaries:

- y^{2} cos (y) + 2 y sin (y) + 2 cos (y) + 2 cos (2) - 4 sin (2)

= - y^{2} cos (y) + 2 y sin (y) + 2 cos (y) + 2 cos (2) - 4 sin (2)

\int_{0}^{3} \frac{1}{3 + 2 ^{x}} d x

\int_{0}^{π} \frac{1}{n} cos (n x) d x

\int_{0}^{1} \frac{x}{2 x} d x

\int_{1}^{3} \frac{1}{( x - 2 ) ^{\frac{5}{3}}} d x

\int_{0}^{π} 5 + sin (x) d x

What is the integral from 2 to y of x^2sin(x) ?
The integral from 2 to y of x^2sin(x) is -y^2cos(y)+2ysin(y)+2cos(y)+2cos(2)-4sin(2)