What is the integral from 1 to x of (2.25)/(x^3) ?

The integral from 1 to x of (2.25)/(x^3) is 2.25(-(0.5)/(x^2)+0.5)

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integral from 1 to x of (2.25)/(x^3)

\int_{1}^{x} \frac{2.25}{x ^{3}} d x

2.25 (- \frac{0.5}{x ^{2}} + 0.5)

Solution steps

\int_{1}^{x} \frac{2.25}{x ^{3}} d x

Take the constant out:

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

= 2.25 \cdot \int_{1}^{x} \frac{1}{x ^{3}} d x

Apply the Power Rule

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

= 2.25 [- \frac{1}{2 x ^{2}}]_{1}^{x}

Simplify

= 2.25 [- \frac{0.5}{x ^{2}}]_{1}^{x}

Compute the boundaries:

- \frac{0.5}{x ^{2}} + 0.5

= 2.25 (- \frac{0.5}{x ^{2}} + 0.5)

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What is the integral from 1 to x of (2.25)/(x^3) ?
The integral from 1 to x of (2.25)/(x^3) is 2.25(-(0.5)/(x^2)+0.5)