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

The integral from 0 to 3 of x^4-3x^2+4x is 198/5

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

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

\frac{198}{5}

Decimal

39.6

Solution steps

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

\int_{0}^{3} x^{4} d x = \frac{243}{5}

\int_{0}^{3} 3 x^{2} d x = 27

\int_{0}^{3} 4 x d x = 18

= \frac{243}{5} - 27 + 18

Simplify

\frac{243}{5} - 27 + 18 : \frac{198}{5}

= \frac{198}{5}

\int_{0}^{1} e^{x^{2}} x d x

\int_{0}^{2} 2 x + 1 d x

\int_{2}^{5} 4 x d x

\int_{- 2}^{2} (x - 1) 4 - x^{2} d x

\int_{0}^{0.5} sin (x) d x

What is the integral from 0 to 3 of x^4-3x^2+4x ?
The integral from 0 to 3 of x^4-3x^2+4x is 198/5