What is the integral from pi/3 to pi/2 of cos(pi)x ?

The integral from pi/3 to pi/2 of cos(pi)x is -(5pi^2)/(72)

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integral from pi/3 to pi/2 of cos(pi)x

\int_{\frac{π}{3}}^{\frac{π}{2}} cos (π) x d x

- \frac{5 π ^{2}}{72}

Decimal

- 0.68538 \dots

Solution steps

\int_{\frac{π}{3}}^{\frac{π}{2}} cos (π) x d x

Take the constant out:

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

= cos (π) \cdot \int_{\frac{π}{3}}^{\frac{π}{2}} x d x

cos (π) = - 1

= (- 1) \cdot \int_{\frac{π}{3}}^{\frac{π}{2}} x d x

Apply the Power Rule

: [\frac{x ^{2}}{2}]_{\frac{π}{3}}^{\frac{π}{2}}

= (- 1) [\frac{x ^{2}}{2}]_{\frac{π}{3}}^{\frac{π}{2}}

Simplify

= - [\frac{x ^{2}}{2}]_{\frac{π}{3}}^{\frac{π}{2}}

Compute the boundaries:

\frac{5 π ^{2}}{72}

= - \frac{5 π ^{2}}{72}

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What is the integral from pi/3 to pi/2 of cos(pi)x ?
The integral from pi/3 to pi/2 of cos(pi)x is -(5pi^2)/(72)