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Popular >

integral from 3 to 6 of (2x+1)^2

Solution

\int_{3}^{6} (2 x + 1)^{2} d x

Solution

309

Solution steps

\int_{3}^{6} (2 x + 1)^{2} d x

Expand

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

= \int_{3}^{6} 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_{3}^{6} 4 x^{2} d x + \int_{3}^{6} 4 x d x + \int_{3}^{6} 1 d x

\int_{3}^{6} 4 x^{2} d x = 252

\int_{3}^{6} 4 x d x = 54

\int_{3}^{6} 1 d x = 3

= 252 + 54 + 3

Simplify

= 309

Graph

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\int_{\infty}^{0} x e^{x} d x

Frequently Asked Questions (FAQ)

What is the integral from 3 to 6 of (2x+1)^2 ?
The integral from 3 to 6 of (2x+1)^2 is 309