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Popular Calculus >

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

Solution

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

Solution

134

Solution steps

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

Expand

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

= \int_{1}^{3} 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_{1}^{3} 9 x^{2} d x + \int_{1}^{3} 12 x d x + \int_{1}^{3} 4 d x

\int_{1}^{3} 9 x^{2} d x = 78

\int_{1}^{3} 12 x d x = 48

\int_{1}^{3} 4 d x = 8

= 78 + 48 + 8

Simplify

= 134

Graph

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Frequently Asked Questions (FAQ)

What is the integral from 1 to 3 of (3x+2)^2 ?
The integral from 1 to 3 of (3x+2)^2 is 134