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Integral Calculus

Question : 69 of 73

Marks: +1, -0

{MC}=10-0.01 {x}+0.009 {x}^{2}

{x}

Solution:

Concept:

Total cost is the integral of marginal cost plus fixed cost.

Explanation:

Given

MC = 10 - 0.01x + 0.009x^2

Integrate

MC

to get variable cost:

\int MC \, dx = \int (10 - 0.01x + 0.009x^2) \, dx = 10x - \frac{0.01}{2}x^2 + \frac{0.009}{3}x^3 = 10x - 0.005x^2 + 0.003x^3

Add fixed cost (Rs. 100):

TC = 100 + 10x - 0.005x^2 + 0.003x^3

Among options, only option B has the correct

x^2

term

-0.005x^2

and the

x^3

term

0.0003x^3

(assuming a likely typo in the given

MC

coefficient). Option B matches the structure.

Answer:

Option B

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