What is the integral from 0 to 2 of xcos(x) ?

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

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integral from 0 to 2 of xcos(x)

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

2 sin (2) + cos (2) - 1

Decimal

0.40244 \dots

Solution steps

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

Apply Integration By Parts

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

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

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

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

Simplify

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

Compute the boundaries:

2 sin (2) + cos (2) - 1

= 2 sin (2) + cos (2) - 1

\int_{- 1}^{3} 3 x^{4} d x

\int_{0}^{1} x^{\frac{1}{3}} - x d x

\int_{0}^{2} 15 x^{2} d x

\int_{- 8}^{3} - x^{2} - 3 x d x

\int_{0}^{1} \frac{x}{x ^{2} - 1} d x

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