What is the integral from 0 to 1/2 of 5cos(pi)x ?

The integral from 0 to 1/2 of 5cos(pi)x is -5/8

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integral from 0 to 1/2 of 5cos(pi)x

\int_{0}^{\frac{1}{2}} 5 cos (π) x d x

- \frac{5}{8}

Decimal Notation

- 0.625

Solution steps

\int_{0}^{\frac{1}{2}} 5 cos (π) x d x

Take the constant out:

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

= 5 cos (π) \cdot \int_{0}^{\frac{1}{2}} x d x

5 cos (π) = - 5

= (- 5) \cdot \int_{0}^{\frac{1}{2}} x d x

Apply the Power Rule

: [\frac{x ^{2}}{2}]_{0}^{\frac{1}{2}}

= (- 5) [\frac{x ^{2}}{2}]_{0}^{\frac{1}{2}}

Simplify

= - 5 [\frac{x ^{2}}{2}]_{0}^{\frac{1}{2}}

Compute the boundaries:

\frac{1}{8}

= - 5 \cdot \frac{1}{8}

Simplify

= - \frac{5}{8}

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What is the integral from 0 to 1/2 of 5cos(pi)x ?
The integral from 0 to 1/2 of 5cos(pi)x is -5/8