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Popular >

integral from 0 to 6 of (x+2)^2

Solution

\int_{0}^{6} (x + 2)^{2} d x

Solution

168

Solution steps

\int_{0}^{6} (x + 2)^{2} d x

Expand

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

= \int_{0}^{6} 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_{0}^{6} x^{2} d x + \int_{0}^{6} 4 x d x + \int_{0}^{6} 4 d x

\int_{0}^{6} x^{2} d x = 72

\int_{0}^{6} 4 x d x = 72

\int_{0}^{6} 4 d x = 24

= 72 + 72 + 24

Simplify

= 168

Popular Examples

integral from 4 to 6 of x^2+2x-11

\int_{4}^{6} x^{2} + 2 x - 11 d x

integral from-2 to 1 of e^{u+2}

\int_{- 2}^{1} e^{u + 2} d u

integral from 1 to 4 of 4^{2x}

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

integral from 1/e to 1 of ln(x)

\int_{\frac{1}{e}}^{1} ln (x) d x

integral from 0 to 2 of-x^3+4x

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

Frequently Asked Questions (FAQ)

What is the integral from 0 to 6 of (x+2)^2 ?
The integral from 0 to 6 of (x+2)^2 is 168