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

The integral from 1 to 2 of 3(2x-1)^2-3 is 10

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integral from 1 to 2 of 3(2x-1)^2-3

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

10

Solution steps

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

Simplify

3 (2 x - 1)^{2} - 3 : 12 x^{2} - 12 x

= \int_{1}^{2} 12 x^{2} - 12 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}^{2} 12 x^{2} d x - \int_{1}^{2} 12 x d x

\int_{1}^{2} 12 x^{2} d x = 28

\int_{1}^{2} 12 x d x = 18

= 28 - 18

Simplify

= 10

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\int_{0}^{x^{2}} e^{x} f (t) d t

What is the integral from 1 to 2 of 3(2x-1)^2-3 ?
The integral from 1 to 2 of 3(2x-1)^2-3 is 10