What is the integral from-42.25 to 0 of (13/2 x)^2 ?

The integral from-42.25 to 0 of (13/2 x)^2 is 1062149.37630…

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integral from-42.25 to 0 of (13/2 x)^2

\int_{- 42.25}^{0} (\frac{13}{2} x)^{2} d x

1062149.37630 \dots

Solution steps

\int_{- 42.25}^{0} (\frac{13}{2} x)^{2} d x

Simplify

(\frac{13}{2} x)^{2} : \frac{169}{4} x^{2}

= \int_{- 42.25}^{0} \frac{169}{4} x^{2} d x

Take the constant out:

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

= \frac{169}{4} \cdot \int_{- 42.25}^{0} x^{2} d x

Apply the Power Rule

: [\frac{x ^{3}}{3}]_{- 42.25}^{0}

= \frac{169}{4} [\frac{x ^{3}}{3}]_{- 42.25}^{0}

Simplify

= 42.25 [0.33333 \dots x^{3}]_{- 42.25}^{0}

Compute the boundaries:

25139.63020 \dots

= 42.25 \cdot 25139.63020 \dots

Simplify

= 1062149.37630 \dots

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What is the integral from-42.25 to 0 of (13/2 x)^2 ?
The integral from-42.25 to 0 of (13/2 x)^2 is 1062149.37630…