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

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

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

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

\frac{1}{2}

Decimal Notation

0.5

Solution steps

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

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

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

= 2 - \frac{3}{2}

Simplify

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

= \frac{1}{2}

\frac{d y}{d x} = \frac{1}{x} (y^{2} + 0.4 y)

\int \frac{x ^{2} - 4 x + 7}{( x + 1 ) ( x ^{2} - 2 x + 3 )} d x

y = 5 tan (x)

t^{2} \frac{d y}{d t} + t y = 4

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

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