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Popular Calculus >

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

Solution

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

Solution

21

Solution steps

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

Expand

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

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

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

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

\int_{- 2}^{1} 9 d x = 27

= 12 - 18 + 27

Simplify

= 21

Graph

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Frequently Asked Questions (FAQ)

What is the integral from-2 to 1 of (2x+3)^2 ?
The integral from-2 to 1 of (2x+3)^2 is 21