What is the integral from 1 to 3 of (3/4 x^2-2) ?

The integral from 1 to 3 of (3/4 x^2-2) is 5/2

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integral from 1 to 3 of (3/4 x^2-2)

\int_{1}^{3} (\frac{3}{4} x^{2} - 2) d x

\frac{5}{2}

Decimal

2.5

Solution steps

\int_{1}^{3} \frac{3}{4} x^{2} - 2 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{1}^{3} \frac{3}{4} x^{2} d x - \int_{1}^{3} 2 d x

\int_{1}^{3} \frac{3}{4} x^{2} d x = \frac{13}{2}

\int_{1}^{3} 2 d x = 4

= \frac{13}{2} - 4

Simplify

\frac{13}{2} - 4 : \frac{5}{2}

= \frac{5}{2}

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What is the integral from 1 to 3 of (3/4 x^2-2) ?
The integral from 1 to 3 of (3/4 x^2-2) is 5/2