What is the integral from 0 to 1 of (5x^3-1/2) ?

The integral from 0 to 1 of (5x^3-1/2) is 3/4

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integral from 0 to 1 of (5x^3-1/2)

\int_{0}^{1} (5 x^{3} - \frac{1}{2}) d x

\frac{3}{4}

Decimal

0.75

Solution steps

\int_{0}^{1} 5 x^{3} - \frac{1}{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_{0}^{1} 5 x^{3} d x - \int_{0}^{1} \frac{1}{2} d x

\int_{0}^{1} 5 x^{3} d x = \frac{5}{4}

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

= \frac{5}{4} - \frac{1}{2}

Simplify

\frac{5}{4} - \frac{1}{2} : \frac{3}{4}

= \frac{3}{4}

\int_{1}^{6} t^{2} - 4 t - 12 d t

\int_{- 7}^{8} \frac{1}{2} x d x

\int_{0}^{6} - \frac{5}{12} x^{2} - 5 x d x

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

\int_{0}^{1} (x - 1) e^{- x} d x

What is the integral from 0 to 1 of (5x^3-1/2) ?
The integral from 0 to 1 of (5x^3-1/2) is 3/4