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

The integral from-pi to pi of xcos(n)x is (2pi^3)/3 cos(n)

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integral from-pi to pi of xcos(n)x

\int_{- π}^{π} x cos (n) x d x

\frac{2 π ^{3}}{3} cos (n)

Solution steps

\int_{- π}^{π} x cos (n) x d x

Take the constant out:

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

= cos (n) \cdot \int_{- π}^{π} xx d x

Simplify

xx : x^{2}

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

Apply the Power Rule

: [\frac{x ^{3}}{3}]_{- π}^{π}

= cos (n) [\frac{x ^{3}}{3}]_{- π}^{π}

Compute the boundaries:

2 \cdot \frac{π ^{3}}{3}

= cos (n) \cdot 2 \cdot \frac{π ^{3}}{3}

Simplify

= \frac{2 π ^{3}}{3} cos (n)

\int_{0}^{s i n (z)} x - 1 d x

\int_{\frac{π}{4}}^{\frac{3 π}{4}} csc (x) d x

\int_{1}^{2} \frac{2 x}{( x ^{2} + 1 ) ^{2}} d x

\int_{- \frac{π}{6}}^{\frac{π}{6}} tan^{3} (x) d x

\int_{- π}^{0} (π + x) d x

What is the integral from-pi to pi of xcos(n)x ?
The integral from-pi to pi of xcos(n)x is (2pi^3)/3 cos(n)