What is the integral from 0 to 2 of 2x^2sqrt(x^3)+1 ?

The integral from 0 to 2 of 2x^2sqrt(x^3)+1 is (64sqrt(2))/9+2

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integral from 0 to 2 of 2x^2sqrt(x^3)+1

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

\frac{64 2}{9} + 2

Decimal

12.05662 \dots

Solution steps

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

\int_{0}^{2} 2 x^{2} x^{3} d x = \frac{64 2}{9}

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

= \frac{64 2}{9} + 2

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What is the integral from 0 to 2 of 2x^2sqrt(x^3)+1 ?
The integral from 0 to 2 of 2x^2sqrt(x^3)+1 is (64sqrt(2))/9+2