What is the integral from-2 to 3 of x^2sin(x) ?

The integral from-2 to 3 of x^2sin(x) is -7cos(3)+6sin(3)+2cos(2)-4sin(2)

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integral from-2 to 3 of x^2sin(x)

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

- 7 cos (3) + 6 sin (3) + 2 cos (2) - 4 sin (2)

Decimal Notation

3.30718 \dots

Solution steps

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

Apply Integration By Parts

: [- x^{2} cos (x) - \int - 2 x cos (x) d x]_{- 2}^{3}

= [- x^{2} cos (x) - \int - 2 x cos (x) d x]_{- 2}^{3}

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

= [- x^{2} cos (x) - (- 2 (x sin (x) + cos (x)))]_{- 2}^{3}

Simplify

= [- x^{2} cos (x) + 2 (x sin (x) + cos (x))]_{- 2}^{3}

Compute the boundaries:

- 7 cos (3) + 6 sin (3) + 2 cos (2) - 4 sin (2)

= - 7 cos (3) + 6 sin (3) + 2 cos (2) - 4 sin (2)

\int_{0}^{\infty} 5 y e^{- 5 y} d y

\int_{0}^{2 π} cos^{2} (4 x) d x

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

\int_{0}^{\frac{π}{2}} e^{- 5 x} sin (x) d x

\int_{1}^{5} \frac{5 x}{x ^{2} + 2} d x

What is the integral from-2 to 3 of x^2sin(x) ?
The integral from-2 to 3 of x^2sin(x) is -7cos(3)+6sin(3)+2cos(2)-4sin(2)