What is the integral from 0 to 3 of xsin(3-x) ?

The integral from 0 to 3 of xsin(3-x) is 3-sin(3)

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integral from 0 to 3 of xsin(3-x)

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

3 - sin (3)

Decimal

2.85887 \dots

Solution steps

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

Apply Integration By Parts

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

\int cos (3 - x) d x = - sin (3 - x)

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

Simplify

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

Compute the boundaries:

3 - sin (3)

= 3 - sin (3)

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

a re a y = 4 x - x^{2}, y = x, x = 3

x \to \infty lim (\frac{0}{3})

d er i v a t i v e f (x) = \frac{x}{x ^{3} + 1}

\int \frac{3}{x ^{2} + 16} d x

What is the integral from 0 to 3 of xsin(3-x) ?
The integral from 0 to 3 of xsin(3-x) is 3-sin(3)