What is the integral from 0 to 1 of x^2cos(x) ?

The integral from 0 to 1 of x^2cos(x) is 2cos(1)-sin(1)

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integral from 0 to 1 of x^2cos(x)

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

2 cos (1) - sin (1)

Decimal

0.23913 \dots

Solution steps

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

Apply Integration By Parts

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

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

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

Compute the boundaries:

2 cos (1) - sin (1)

= 2 cos (1) - sin (1)

What is the integral from 0 to 1 of x^2cos(x) ?
The integral from 0 to 1 of x^2cos(x) is 2cos(1)-sin(1)