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

The integral from 2 to 4 of x^3+4x^2 is 404/3

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

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

\frac{404}{3}

Decimal

134.66666 \dots

Solution steps

\int_{2}^{4} x^{3} + 4 x^{2} 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_{2}^{4} x^{3} d x + \int_{2}^{4} 4 x^{2} d x

\int_{2}^{4} x^{3} d x = 60

\int_{2}^{4} 4 x^{2} d x = \frac{224}{3}

= 60 + \frac{224}{3}

Simplify

60 + \frac{224}{3} : \frac{404}{3}

= \frac{404}{3}

What is the integral from 2 to 4 of x^3+4x^2 ?
The integral from 2 to 4 of x^3+4x^2 is 404/3