Business I / Integral Calculus

Practice question · Match the pairs

Match each integral to its business meaning.

$\int_0^q MC(x)\,dx$
$\int_0^{q^*}(D - p^*)\,dq$
$\int_{q_1}^{q_2} M\pi(q)\,dq$
$\int_0^{30} s(t)\,dt$

Extra profit from raising output
Units sold over a 30-day month
Total variable cost of producing $q$
Consumer surplus

Hints

Each is an area under a rate or a margin.
Ask what the height of the curve represents in each case.

Show the answer

$\int_0^q MC(x)\,dx$ → Total variable cost of producing $q$
$\int_0^{q^*}(D - p^*)\,dq$ → Consumer surplus
$\int_{q_1}^{q_2} M\pi(q)\,dq$ → Extra profit from raising output
$\int_0^{30} s(t)\,dt$ → Units sold over a 30-day month

Why

Same symbol, four dashboards: cost, welfare, profit deltas, and volumes, all areas under a margin or rate.

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