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

The integral from 1 to 4 of (3x^2+3sqrt(x)) is 77

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

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

77

Solution steps

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

\int_{1}^{4} 3 x^{2} d x = 63

\int_{1}^{4} 3 x d x = 14

= 63 + 14

Simplify

= 77

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What is the integral from 1 to 4 of (3x^2+3sqrt(x)) ?
The integral from 1 to 4 of (3x^2+3sqrt(x)) is 77