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

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

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integral from 0 to 1 of (4x-3x^3)

\int_{0}^{1} (4 x - 3 x^{3}) d x

\frac{5}{4}

Decimal Notation

1.25

Solution steps

\int_{0}^{1} 4 x - 3 x^{3} 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} 4 x d x - \int_{0}^{1} 3 x^{3} d x

\int_{0}^{1} 4 x d x = 2

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

= 2 - \frac{3}{4}

Simplify

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

= \frac{5}{4}

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