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

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

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

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

4

Solution steps

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

\int_{0}^{2} x^{3} d x = 4

\int_{0}^{2} 3 x^{2} d x = 8

\int_{0}^{2} 4 d x = 8

= 4 - 8 + 8

Simplify

= 4

y^{^{'}} - \frac{5 y}{x} = 3 x^{4}, y (1) = 5

2 x \frac{d y}{d x} = (cos^{2} (y))

x \to 0 + lim (\frac{5}{1 + x})

\frac{3 z - sin ( z )}{- e ^{z}}

\int 2 e^{x} 9 + e^{x} d x

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