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Popular >

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

Solution

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

Solution

\frac{49}{3}

+1

Decimal

16.33333 \dots

Solution steps

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

Expand

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

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

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

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

\int_{1}^{2} 4 x^{2} d x = \frac{28}{3}

= 1 + 6 + \frac{28}{3}

Simplify

1 + 6 + \frac{28}{3} : \frac{49}{3}

= \frac{49}{3}

Graph

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Frequently Asked Questions (FAQ)

What is the integral from 1 to 2 of (1+2x)^2 ?
The integral from 1 to 2 of (1+2x)^2 is 49/3