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

The integral from 4 to x^2 of (3t^2+2t) is x^6+x^4-80

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

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

x^{6} + x^{4} - 80

Solution steps

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int_{4}^{x^{2}} 3 t^{2} d t = x^{6} - 64

\int_{4}^{x^{2}} 2 t d t = x^{4} - 16

= x^{6} - 64 + x^{4} - 16

Simplify

= x^{6} + x^{4} - 80

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What is the integral from 4 to x^2 of (3t^2+2t) ?
The integral from 4 to x^2 of (3t^2+2t) is x^6+x^4-80