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

The integral from 0 to 1 of sqrt(x)-x^3 is 5/12

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

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

\frac{5}{12}

Decimal

0.41666 \dots

Solution steps

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

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

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

= \frac{2}{3} - \frac{1}{4}

Simplify

\frac{2}{3} - \frac{1}{4} : \frac{5}{12}

= \frac{5}{12}

y^{^{'}} (1 + x^{2}) + (1 + y^{2}) = 0

\int - \frac{2 x}{3} + 2 d x

x \to - 2 + lim (\frac{2}{x ^{2} - 4})

x \frac{d y}{d x} + y = x^{4} y^{3}

y^{^{'}} + 2 x^{2} = 0

What is the integral from 0 to 1 of sqrt(x)-x^3 ?
The integral from 0 to 1 of sqrt(x)-x^3 is 5/12