What is the integral from 0 to 3 of (1/2 x^2-1) ?

The integral from 0 to 3 of (1/2 x^2-1) is 3/2

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integral from 0 to 3 of (1/2 x^2-1)

\int_{0}^{3} (\frac{1}{2} x^{2} - 1) d x

\frac{3}{2}

Decimal

1.5

Solution steps

\int_{0}^{3} \frac{1}{2} x^{2} - 1 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_{0}^{3} \frac{1}{2} x^{2} d x - \int_{0}^{3} 1 d x

\int_{0}^{3} \frac{1}{2} x^{2} d x = \frac{9}{2}

\int_{0}^{3} 1 d x = 3

= \frac{9}{2} - 3

Simplify

\frac{9}{2} - 3 : \frac{3}{2}

= \frac{3}{2}

\int_{0}^{2} (6 x - 6) (4 x^{2} + 3) d x

\int_{0}^{2} x \frac{1}{2} x d x

\int_{- 5}^{5} (2 x + 10) d x

\int_{1}^{16} \frac{5}{x} d x

\int_{- \frac{a}{2}}^{\frac{a}{2}} 1 d x

What is the integral from 0 to 3 of (1/2 x^2-1) ?
The integral from 0 to 3 of (1/2 x^2-1) is 3/2