What is the integral from 0 to 1 of x^3cos(x) ?

The integral from 0 to 1 of x^3cos(x) is -5sin(1)-3cos(1)+6

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integral from 0 to 1 of x^3cos(x)

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

- 5 sin (1) - 3 cos (1) + 6

Decimal Notation

0.17173 \dots

Solution steps

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

Apply Integration By Parts

: [x^{3} sin (x) - \int 3 x^{2} sin (x) d x]_{0}^{1}

= [x^{3} sin (x) - \int 3 x^{2} sin (x) d x]_{0}^{1}

\int 3 x^{2} sin (x) d x = 3 (- x^{2} cos (x) + 2 (x sin (x) + cos (x)))

= [x^{3} sin (x) - 3 (- x^{2} cos (x) + 2 (x sin (x) + cos (x)))]_{0}^{1}

Compute the boundaries:

- 5 sin (1) - 3 cos (1) + 6

= - 5 sin (1) - 3 cos (1) + 6

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\int_{- 1}^{1} - 60 x^{2} d x

What is the integral from 0 to 1 of x^3cos(x) ?
The integral from 0 to 1 of x^3cos(x) is -5sin(1)-3cos(1)+6