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

The integral from 0 to 2 of (x^4-5x^3+2x) is -48/5

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integral from 0 to 2 of (x^4-5x^3+2x)

\int_{0}^{2} (x^{4} - 5 x^{3} + 2 x) d x

- \frac{48}{5}

Decimal Notation

- 9.6

Solution steps

\int_{0}^{2} x^{4} - 5 x^{3} + 2 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}^{2} x^{4} d x - \int_{0}^{2} 5 x^{3} d x + \int_{0}^{2} 2 x d x

\int_{0}^{2} x^{4} d x = \frac{32}{5}

\int_{0}^{2} 5 x^{3} d x = 20

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

= \frac{32}{5} - 20 + 4

Simplify

\frac{32}{5} - 20 + 4 : - \frac{48}{5}

= - \frac{48}{5}

\int \frac{sin ( 2 x )}{43 + cos ^{2} ( x )} d x

y^{^{'}} + 4 y = cos (x)

ln (\frac{x}{2}), at 2

\frac{d y}{d x} = \frac{5 y}{2 x}

4 x^{5}, at (a = 3)

What is the integral from 0 to 2 of (x^4-5x^3+2x) ?
The integral from 0 to 2 of (x^4-5x^3+2x) is -48/5