Water is pumped into a holding tank at a rate modeled by Q(t)=t 1+t^ 2 (liters per…

MATHEMATICS · Multi-part · CBSE · Mathematics · Integrals · Integrals

Problem

Water is pumped into a holding tank at a rate modeled by Q(t)=t1+t2(liters per minute),0≤t≤3.Q(t)=t\sqrt{1+t^{2}}\quad\text{(liters per minute)}, \qquad 0\le t\le 3. (a) Evaluate ∫03Q(t) dt\displaystyle \int_{0}^{3} Q(t)\,dt exactly. (b) Compare your answer from part (a) with the tank capacity and state whether an overflow occurs, supporting your answer with quantitative reasoning.

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