What is the integral from 0 to 1 of cos(pi)t ?

The integral from 0 to 1 of cos(pi)t is -1/2

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integral from 0 to 1 of cos(pi)t

\int_{0}^{1} cos (π) t d t

- \frac{1}{2}

Decimal

- 0.5

Solution steps

\int_{0}^{1} cos (π) t d t

Take the constant out:

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

= cos (π) \cdot \int_{0}^{1} t d t

cos (π) = - 1

= (- 1) \cdot \int_{0}^{1} t d t

Apply the Power Rule

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

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

Simplify

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

Compute the boundaries:

\frac{1}{2}

= - \frac{1}{2}

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