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

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

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

\int_{0}^{π} x^{2} cos (x + 1) d x

π^{2} sin (π + 1) - 2 (- π cos (π + 1) + sin (π + 1)) + 2 sin (1)

Decimal Notation

- 8.33392 \dots

Solution steps

\int_{0}^{π} x^{2} cos (x + 1) d x

Apply Integration By Parts

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

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

\int 2 x sin (x + 1) d x = 2 (- x cos (x + 1) + sin (x + 1))

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

Compute the boundaries:

π^{2} sin (π + 1) - 2 (- π cos (π + 1) + sin (π + 1)) + 2 sin (1)

= π^{2} sin (π + 1) - 2 (- π cos (π + 1) + sin (π + 1)) + 2 sin (1)

\int_{4}^{6} \frac{1}{x - 4} d x

\int_{0}^{2 π} sin^{3} (θ) d θ

\int_{0}^{\frac{π}{3}} sin^{3} (3 x) d x

\int_{0}^{1} x^{2} e^{- 13 x} d x

\int_{0}^{1} \frac{x - 4}{x ^{2} + 5 x + 6} d x

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