What is the integral from 10 to x of 9t^2 ?

The integral from 10 to x of 9t^2 is 3(x^3-1000)

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integral from 10 to x of 9t^2

\int_{10}^{x} 9 t^{2} d t

3 (x^{3} - 1000)

Solution steps

\int_{10}^{x} 9 t^{2} d t

Take the constant out:

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

= 9 \cdot \int_{10}^{x} t^{2} d t

Apply the Power Rule

: [\frac{t ^{3}}{3}]_{10}^{x}

= 9 [\frac{t ^{3}}{3}]_{10}^{x}

Compute the boundaries:

\frac{x ^{3}}{3} - \frac{1000}{3}

= 9 (\frac{x ^{3}}{3} - \frac{1000}{3})

Simplify

= 3 (x^{3} - 1000)

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What is the integral from 10 to x of 9t^2 ?
The integral from 10 to x of 9t^2 is 3(x^3-1000)