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

The integral from 0 to 2 of (x-3)(x-5) is 50/3

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integral from 0 to 2 of (x-3)(x-5)

\int_{0}^{2} (x - 3) (x - 5) d x

\frac{50}{3}

Decimal

16.66666 \dots

Solution steps

\int_{0}^{2} (x - 3) (x - 5) d x

Expand

(x - 3) (x - 5) : x^{2} - 8 x + 15

= \int_{0}^{2} x^{2} - 8 x + 15 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} 8 x d x + \int_{0}^{2} 15 d x

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

\int_{0}^{2} 8 x d x = 16

\int_{0}^{2} 15 d x = 30

= \frac{8}{3} - 16 + 30

Simplify

\frac{8}{3} - 16 + 30 : \frac{50}{3}

= \frac{50}{3}

What is the integral from 0 to 2 of (x-3)(x-5) ?
The integral from 0 to 2 of (x-3)(x-5) is 50/3