What is the integral from 1 to 2 of (3x^2+4x^3) ?

The integral from 1 to 2 of (3x^2+4x^3) is 22

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integral from 1 to 2 of (3x^2+4x^3)

\int_{1}^{2} (3 x^{2} + 4 x^{3}) d x

22

Solution steps

\int_{1}^{2} 3 x^{2} + 4 x^{3} 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_{1}^{2} 3 x^{2} d x + \int_{1}^{2} 4 x^{3} d x

\int_{1}^{2} 3 x^{2} d x = 7

\int_{1}^{2} 4 x^{3} d x = 15

= 7 + 15

Simplify

= 22

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What is the integral from 1 to 2 of (3x^2+4x^3) ?
The integral from 1 to 2 of (3x^2+4x^3) is 22