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

The integral from 0 to 2pi of 2xcos(x) is 0

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integral from 0 to 2pi of 2xcos(x)

\int_{0}^{2 π} 2 x cos (x) d x

0

Solution steps

\int_{0}^{2 π} 2 x cos (x) d x

Take the constant out:

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

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

Apply Integration By Parts

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

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

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

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

Simplify

= 2 [x sin (x) + cos (x)]_{0}^{2 π}

Compute the boundaries:

0

= 2 \cdot 0

Simplify

= 0

\int_{2}^{4} x - 9 d x

\int_{0}^{1} (1 - 4 x) d x

\int_{0}^{2 π} (1 - sin (x))^{2} d x

\int_{3 + 4 x}^{5 x} 1 d x

\int_{0}^{b} \frac{1}{x ^{2} + b ^{2}} d x

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