What is the integral from 0 to pi of cos(n)x ?

The integral from 0 to pi of cos(n)x is cos(n)(pi^2)/2

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integral from 0 to pi of cos(n)x

\int_{0}^{π} cos (n) x d x

cos (n) \frac{π ^{2}}{2}

Solution steps

\int_{0}^{π} 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_{0}^{π} x d x

Apply the Power Rule

: [\frac{x ^{2}}{2}]_{0}^{π}

= cos (n) [\frac{x ^{2}}{2}]_{0}^{π}

Compute the boundaries:

\frac{π ^{2}}{2}

= cos (n) \frac{π ^{2}}{2}

\int_{2}^{3} (3 x^{2} - \frac{x ^{3}}{4}) d x

\int_{0}^{2 π} - 4 d t

\int_{- 1}^{1} e^{x} - e^{- x} d x

\int_{- 7}^{7} ∣ x ∣ d x

\int_{- 2}^{0} x^{2} + x d x

What is the integral from 0 to pi of cos(n)x ?
The integral from 0 to pi of cos(n)x is cos(n)(pi^2)/2