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Popular Calculus >

integral from 0 to 2 of (2x-5)^2

Solution

\int_{0}^{2} (2 x - 5)^{2} d x

Solution

\frac{62}{3}

+1

Decimal

20.66666 \dots

Solution steps

\int_{0}^{2} (2 x - 5)^{2} d x

Expand

(2 x - 5)^{2} : 4 x^{2} - 20 x + 25

= \int_{0}^{2} 4 x^{2} - 20 x + 25 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} 4 x^{2} d x - \int_{0}^{2} 20 x d x + \int_{0}^{2} 25 d x

\int_{0}^{2} 4 x^{2} d x = \frac{32}{3}

\int_{0}^{2} 20 x d x = 40

\int_{0}^{2} 25 d x = 50

= \frac{32}{3} - 40 + 50

Simplify

\frac{32}{3} - 40 + 50 : \frac{62}{3}

= \frac{62}{3}

Graph

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Frequently Asked Questions (FAQ)

What is the integral from 0 to 2 of (2x-5)^2 ?
The integral from 0 to 2 of (2x-5)^2 is 62/3