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Popular Calculus >

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

Solution

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

Solution

21

Solution steps

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

Expand

(2 x + 1)^{2} : 4 x^{2} + 4 x + 1

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

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

\int_{- 1}^{2} 4 x d x = 6

\int_{- 1}^{2} 1 d x = 3

= 12 + 6 + 3

Simplify

= 21

Graph

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Frequently Asked Questions (FAQ)

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