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Popular >

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

Popular Examples

integral from 2 to 3 of 4-x^2

\int_{2}^{3} 4 - x^{2} d x

integral from-1 to 1 of |x^2-x|

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

integral from 1 to 2 of 1/(x+1)

\int_{1}^{2} \frac{1}{x + 1} d x

integral from 0 to 1 of (e^z+7)/(e^z+7z)

\int_{0}^{1} \frac{e ^{z} + 7}{e ^{z} + 7 z} d z

integral from 0 to 2 of 1/(sqrt(2x-x^2))

\int_{0}^{2} \frac{1}{2 x - x ^{2}} d x

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