What is the integral from 0 to 5 of (x-20)(10x-50) ?

The integral from 0 to 5 of (x-20)(10x-50) is 6875/3

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integral from 0 to 5 of (x-20)(10x-50)

\int_{0}^{5} (x - 20) (10 x - 50) d x

\frac{6875}{3}

Decimal Notation

2291.66666 \dots

Solution steps

\int_{0}^{5} (x - 20) (10 x - 50) d x

Expand

(x - 20) (10 x - 50) : 10 x^{2} - 250 x + 1000

= \int_{0}^{5} 10 x^{2} - 250 x + 1000 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}^{5} 10 x^{2} d x - \int_{0}^{5} 250 x d x + \int_{0}^{5} 1000 d x

\int_{0}^{5} 10 x^{2} d x = \frac{1250}{3}

\int_{0}^{5} 250 x d x = 3125

\int_{0}^{5} 1000 d x = 5000

= \frac{1250}{3} - 3125 + 5000

Simplify

\frac{1250}{3} - 3125 + 5000 : \frac{6875}{3}

= \frac{6875}{3}

\int \frac{x ^{2}}{1 + x} d x

f (x) = 3 x^{4} - 5 x^{3} - x^{2} + 4 x + 9

\int \frac{x}{x + 6} d x

\int \frac{4 cos ( x )}{sin ^{2} ( x )} d x

y = cos (x), at x = 1

What is the integral from 0 to 5 of (x-20)(10x-50) ?
The integral from 0 to 5 of (x-20)(10x-50) is 6875/3