What is the integral from 0 to 2 of x^2sin(x) ?

The integral from 0 to 2 of x^2sin(x) is -2cos(2)+4sin(2)-2

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integral from 0 to 2 of x^2sin(x)

\int_{0}^{2} x^{2} sin (x) d x

- 2 cos (2) + 4 sin (2) - 2

Decimal Notation

2.46948 \dots

Solution steps

\int_{0}^{2} x^{2} sin (x) d x

Apply Integration By Parts

: [- x^{2} cos (x) - \int - 2 x cos (x) d x]_{0}^{2}

= [- x^{2} cos (x) - \int - 2 x cos (x) d x]_{0}^{2}

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

= [- x^{2} cos (x) - (- 2 (x sin (x) + cos (x)))]_{0}^{2}

Simplify

= [- x^{2} cos (x) + 2 (x sin (x) + cos (x))]_{0}^{2}

Compute the boundaries:

- 2 cos (2) + 4 sin (2) - 2

= - 2 cos (2) + 4 sin (2) - 2

\int_{0}^{2 π} e^{2 x} d x

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

\int_{0}^{2} \frac{x ^{3}}{x ^{4} + 6} d x

\int_{4}^{6} 30 x^{3} 1 + x^{2} d x

\int_{- \infty}^{0} x^{2} d x

What is the integral from 0 to 2 of x^2sin(x) ?
The integral from 0 to 2 of x^2sin(x) is -2cos(2)+4sin(2)-2