What is the integral from 1 to 100 of 9/(x^3) ?

The integral from 1 to 100 of 9/(x^3) is 89991/20000

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integral from 1 to 100 of 9/(x^3)

\int_{1}^{100} \frac{9}{x ^{3}} d x

\frac{89991}{20000}

Decimal Notation

4.49955

Solution steps

\int_{1}^{100} \frac{9}{x ^{3}} d x

Take the constant out:

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

= 9 \cdot \int_{1}^{100} \frac{1}{x ^{3}} d x

Apply the Power Rule

: [- \frac{1}{2 x ^{2}}]_{1}^{100}

= 9 [- \frac{1}{2 x ^{2}}]_{1}^{100}

Compute the boundaries:

\frac{9999}{20000}

= 9 \cdot \frac{9999}{20000}

Simplify

= \frac{89991}{20000}

f (x) = 3 x^{2} + 32 x + 64

3 x^{3}, [0, 6]

\int x (x^{2} - 3 x - 5) d x

f (x) = 2^{x}

\frac{\partial}{\partial s} (rs e^{t})

What is the integral from 1 to 100 of 9/(x^3) ?
The integral from 1 to 100 of 9/(x^3) is 89991/20000