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

The integral from 1 to 3 of x(2.25)/(x^3) is 1.5

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

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

1.5

Solution steps

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

Simplify

x \frac{1}{x ^{3}} : \frac{1}{x ^{2}}

= 2.25 \cdot \int_{1}^{3} \frac{1}{x ^{2}} d x

Apply the Power Rule

= 2.25 [- \frac{1}{x}]_{1}^{3}

Compute the boundaries:

\frac{2}{3}

= 2.25 \cdot \frac{2}{3}

Simplify

= 1.5

What is the integral from 1 to 3 of x(2.25)/(x^3) ?
The integral from 1 to 3 of x(2.25)/(x^3) is 1.5