What is the integral from 3 to 4 of x^2sin(x) ?

The integral from 3 to 4 of x^2sin(x) is -14cos(4)+8sin(4)+7cos(3)-6sin(3)

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integral from 3 to 4 of x^2sin(x)

\int_{3}^{4} x^{2} sin (x) d x

- 14 cos (4) + 8 sin (4) + 7 cos (3) - 6 sin (3)

Decimal Notation

- 4.68007 \dots

Solution steps

\int_{3}^{4} x^{2} sin (x) d x

Apply Integration By Parts

: [- x^{2} cos (x) - \int - 2 x cos (x) d x]_{3}^{4}

= [- x^{2} cos (x) - \int - 2 x cos (x) d x]_{3}^{4}

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

= [- x^{2} cos (x) - (- 2 (x sin (x) + cos (x)))]_{3}^{4}

Simplify

= [- x^{2} cos (x) + 2 (x sin (x) + cos (x))]_{3}^{4}

Compute the boundaries:

- 14 cos (4) + 8 sin (4) + 7 cos (3) - 6 sin (3)

= - 14 cos (4) + 8 sin (4) + 7 cos (3) - 6 sin (3)

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

\int_{1}^{3} \frac{x - 3}{x} d x

\int_{1}^{4} (x^{2} + 2 x + 1) d x

\int_{0}^{30} cos (5 x) d x

\int_{0}^{4} - x^{2} + 2 x + 4 x d x

What is the integral from 3 to 4 of x^2sin(x) ?
The integral from 3 to 4 of x^2sin(x) is -14cos(4)+8sin(4)+7cos(3)-6sin(3)