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Popular >

integral from 0 to 2 of (x-7)^2

Solution

\int_{0}^{2} (x - 7)^{2} d x

Solution

\frac{218}{3}

+1

Decimal

72.66666 \dots

Solution steps

\int_{0}^{2} (x - 7)^{2} d x

Expand

(x - 7)^{2} : x^{2} - 14 x + 49

= \int_{0}^{2} x^{2} - 14 x + 49 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}^{2} x^{2} d x - \int_{0}^{2} 14 x d x + \int_{0}^{2} 49 d x

\int_{0}^{2} x^{2} d x = \frac{8}{3}

\int_{0}^{2} 14 x d x = 28

\int_{0}^{2} 49 d x = 98

= \frac{8}{3} - 28 + 98

Simplify

\frac{8}{3} - 28 + 98 : \frac{218}{3}

= \frac{218}{3}

Graph

Popular Examples

integral of \sqrt[3]{ax}

\int 3 a x d x

limit as x approaches 3-of 1/(x^2-9)

x \to 3 - lim (\frac{1}{x ^{2} - 9})

limit as x approaches 2 of (4-x^2)/x

x \to 2 lim (\frac{4 - x ^{2}}{x})

tangent of y=x+sqrt(x),(16,20)tangent of

y = x + x, (16, 20)

(dy)/(dx)+e^xy=1

\frac{d y}{d x} + e^{x} y = 1

Frequently Asked Questions (FAQ)

What is the integral from 0 to 2 of (x-7)^2 ?
The integral from 0 to 2 of (x-7)^2 is 218/3