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Calculating The Area Between Two Curves Using Definite Integrals

Get step-by-step Homework Answers on finding areas between curves.

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Calculating the Area Between Two Curves Using Definite IntegralsConsider the following expression for the area of a region between two curves:Area=∫−243[4x−(2x−4)]dx+∫434[(−12x+6)−(2x−4)]dx\text{Area} =\int_{-2}^{\frac{4}{3}}\left[ 4x-(2x-4)\right]\, dx +\int_{\frac{4}{3}}^4\left[\left(-\frac{1}{2} x + 6\right)-(2x-4)\right]\, dxSimplify and compute the area under the curves described by the integrals. Show all your steps andprovide the final answer.Hint:Simplify the integrals step by step before calculating the area. Also, ensure to compute theindividual integrals properly.What is the total area represented by the integrals?Answer:1.Graph:Area =∫[4𝑥−(2𝑥−4)]𝑑𝑥+∫[(−12𝑥+6)−(2𝑥−4)]443⁄43⁄−2𝑑𝑥=∫(2𝑥+4)𝑑𝑥+∫(−52𝑥+10)443⁄43⁄−2𝑑𝑥=20

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