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

The integral from 1 to 3 of x^2(2.25)/(x^3) is 2.47187…

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integral from 1 to 3 of x^2(2.25)/(x^3)

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

2.47187 \dots

Solution steps

\int_{1}^{3} x^{2} \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^{2} \frac{1}{x ^{3}} d x

Simplify

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

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

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= 2.25 [ln ∣ x ∣]_{1}^{3}

Compute the boundaries:

ln (3)

= 2.25 ln (3)

Simplify

= 2.47187 \dots

What is the integral from 1 to 3 of x^2(2.25)/(x^3) ?
The integral from 1 to 3 of x^2(2.25)/(x^3) is 2.47187…