What is the integral from 0 to 2 of 5tcos(pi*t) ?

The integral from 0 to 2 of 5tcos(pi*t) is 0

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integral from 0 to 2 of 5tcos(pi*t)

\int_{0}^{2} 5 t cos (π \cdot t) d t

0

Solution steps

\int_{0}^{2} 5 t cos (π t) d t

Take the constant out:

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

= 5 \cdot \int_{0}^{2} t cos (π t) d t

Apply Integration By Parts

: [\frac{1}{π} t sin (π t) - \int \frac{1}{π} sin (π t) d t]_{0}^{2}

= 5 [\frac{1}{π} t sin (π t) - \int \frac{1}{π} sin (π t) d t]_{0}^{2}

\int \frac{1}{π} sin (π t) d t = - \frac{1}{π ^{2}} cos (π t)

= 5 [\frac{1}{π} t sin (π t) - (- \frac{1}{π ^{2}} cos (π t))]_{0}^{2}

Simplify

= 5 [\frac{1}{π} t sin (π t) + \frac{1}{π ^{2}} cos (π t)]_{0}^{2}

Compute the boundaries:

0

= 5 \cdot 0

Simplify

= 0

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What is the integral from 0 to 2 of 5tcos(pi*t) ?
The integral from 0 to 2 of 5tcos(pi*t) is 0