What is the integral from 1 to 2 of pi(x^{-1251})^2 ?

The integral from 1 to 2 of pi(x^{-1251})^2 is pi(-1/(2^{2501)*2501}+1/2501)

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integral from 1 to 2 of pi(x^{-1251})^2

\int_{1}^{2} π (x^{- 1251})^{2} d x

π (- \frac{1}{2 ^{2501} \cdot 2501} + \frac{1}{2501})

Solution steps

\int_{1}^{2} π (x^{- 1251})^{2} d x

Take the constant out:

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

= π \cdot \int_{1}^{2} (x^{- 1251})^{2} d x

Simplify

(x^{- 1251})^{2} : \frac{1}{x ^{2502}}

= π \cdot \int_{1}^{2} \frac{1}{x ^{2502}} d x

Apply the Power Rule

: [- \frac{1}{2501 x ^{2501}}]_{1}^{2}

= π [- \frac{1}{2501 x ^{2501}}]_{1}^{2}

Compute the boundaries:

- \frac{1}{2 ^{2501} \cdot 2501} + \frac{1}{2501}

= π (- \frac{1}{2 ^{2501} \cdot 2501} + \frac{1}{2501})

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What is the integral from 1 to 2 of pi(x^{-1251})^2 ?
The integral from 1 to 2 of pi(x^{-1251})^2 is pi(-1/(2^{2501)*2501}+1/2501)