What is the integral from 0 to 2pi of 6x^2cos(x) ?

The integral from 0 to 2pi of 6x^2cos(x) is 24pi

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integral from 0 to 2pi of 6x^2cos(x)

\int_{0}^{2 π} 6 x^{2} cos (x) d x

24 π

Decimal

75.39822 \dots

Solution steps

\int_{0}^{2 π} 6 x^{2} cos (x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 6 \cdot \int_{0}^{2 π} x^{2} cos (x) d x

Apply Integration By Parts

= 6 [x^{2} sin (x) - \int 2 x sin (x) d x]_{0}^{2 π}

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

= 6 [x^{2} sin (x) - 2 (- x cos (x) + sin (x))]_{0}^{2 π}

Compute the boundaries:

4 π

= 6 \cdot 4 π

Simplify

= 24 π

What is the integral from 0 to 2pi of 6x^2cos(x) ?
The integral from 0 to 2pi of 6x^2cos(x) is 24pi