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Popular >

integral from 0 to 3 of (4x-1)^2

Solution

\int_{0}^{3} (4 x - 1)^{2} d x

Solution

111

Solution steps

\int_{0}^{3} (4 x - 1)^{2} d x

Expand

(4 x - 1)^{2} : 16 x^{2} - 8 x + 1

= \int_{0}^{3} 16 x^{2} - 8 x + 1 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}^{3} 16 x^{2} d x - \int_{0}^{3} 8 x d x + \int_{0}^{3} 1 d x

\int_{0}^{3} 16 x^{2} d x = 144

\int_{0}^{3} 8 x d x = 36

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

= 144 - 36 + 3

Simplify

= 111

Graph

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\int_{0}^{2} 3 + 6 x - x^{3} d x

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Frequently Asked Questions (FAQ)

What is the integral from 0 to 3 of (4x-1)^2 ?
The integral from 0 to 3 of (4x-1)^2 is 111