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Popular >

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

Solution

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

Solution

\frac{37}{3}

+1

Decimal

12.33333 \dots

Solution steps

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

Expand

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

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

\int_{1}^{2} x^{2} d x = \frac{7}{3}

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

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

= \frac{7}{3} + 6 + 4

Simplify

\frac{7}{3} + 6 + 4 : \frac{37}{3}

= \frac{37}{3}

Graph

Popular Examples

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\int_{0}^{1} (x^{2} - 3 x + 4) d x

integral from 0 to r of r^2

\int_{0}^{r} r^{2} d r

integral from 0 to 3 of 1/((x-2)^2)

\int_{0}^{3} \frac{1}{( x - 2 ) ^{2}} d x

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

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

integral from 0 to pi of tsin(nt)

\int_{0}^{π} t sin (n t) d t

Frequently Asked Questions (FAQ)

What is the integral from 1 to 2 of (x+2)^2 ?
The integral from 1 to 2 of (x+2)^2 is 37/3