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

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

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

\int_{- \frac{π}{2}}^{\frac{π}{2}} x cos (2 x) d x

0

Solution steps

\int_{- \frac{π}{2}}^{\frac{π}{2}} x cos (2 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 (2 x) :

Odd

= 0

\int_{9}^{0} ∣ 2 x - 9 ∣ d x

\int_{2}^{10} \frac{3}{5 x - 1} d x

\int_{2}^{4} \frac{1}{x ^{2} - 4} d x

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

\int_{- 6}^{4} \frac{3}{x ^{4}} d x

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