Integrals Problem

Question

The marginal cost of manufacturing x yards of a certain fabric is C′(x)=3−0.01x+0.000006x^2 (in dollars per yard). Find the increase in cost if the production level is raised from 1500 to 9500 yards.

Increase in cost = $

Answer 1

ΔC = ∫₁₅₀₀⁹⁵⁰⁰(3 - 0.01x + 0.000006x²)dx = (3x - 0.005x² + 0.000002x³)₁₅₀₀⁹⁵⁰⁰= $1292000