What is the integral from-2pi to 2pi of xcos(0.5x) ?

The integral from-2pi to 2pi of xcos(0.5x) is 0

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integral from-2pi to 2pi of xcos(0.5x)

\int_{- 2 π}^{2 π} x cos (0.5 x) d x

0

Solution steps

\int_{- 2 π}^{2 π} x cos (0.5 x) d x

If f(x) is an odd function and continuous at:

[- a, a]

then

\int_{- a}^{a} f (x) d x = 0

Parity of

x cos (0.5 x) :

Odd

= 0

\int_{0}^{\frac{4}{9}} \frac{1}{81 x ^{2} + 16} d x

\int_{0}^{l} x sin (\frac{nπ x}{l}) d x

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

\int_{0}^{π} (2 x - 1) cos (3 x) d x

\int_{- π}^{π} 2 sin (x) d x

What is the integral from-2pi to 2pi of xcos(0.5x) ?
The integral from-2pi to 2pi of xcos(0.5x) is 0