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Popular >

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

Solution

\int_{0}^{1} (3 x - 2)^{2} d x

Solution

1

Solution steps

\int_{0}^{1} (3 x - 2)^{2} d x

Expand

(3 x - 2)^{2} : 9 x^{2} - 12 x + 4

= \int_{0}^{1} 9 x^{2} - 12 x + 4 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}^{1} 9 x^{2} d x - \int_{0}^{1} 12 x d x + \int_{0}^{1} 4 d x

\int_{0}^{1} 9 x^{2} d x = 3

\int_{0}^{1} 12 x d x = 6

\int_{0}^{1} 4 d x = 4

= 3 - 6 + 4

Simplify

= 1

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Frequently Asked Questions (FAQ)

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