Evaluate
\frac{3125}{6}\approx 520.833333333
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\int \frac{25x}{9}\mathrm{d}x
Evaluate the indefinite integral first.
\frac{25\int x\mathrm{d}x}{9}
Factor out the constant using \int af\left(x\right)\mathrm{d}x=a\int f\left(x\right)\mathrm{d}x.
\frac{25x^{2}}{18}
Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x\mathrm{d}x with \frac{x^{2}}{2}.
\frac{25}{18}\times 40^{2}-\frac{25}{18}\times 35^{2}
The definite integral is the antiderivative of the expression evaluated at the upper limit of integration minus the antiderivative evaluated at the lower limit of integration.
\frac{3125}{6}
Simplify.
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