Calculating The Area Between Two Curves Using Definite Integrals

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Calculating the Area Between Two Curves Using Definite Integrals Consider 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] \ , dx Simplify and compute the area under the curves described by the integrals. Show all your steps and provide the final answer. Hint: Simplify the integrals step by step before calculating the area. Also, ensure to compute the individual integrals properly. What is the total area represented by the integrals? Answer: 1. Graph: Area = ∫ [ 4 𝑥 − ( 2 𝑥 − 4 ) ] 𝑑𝑥 + ∫ [ ( − 1 2 𝑥 + 6 ) − ( 2 𝑥 − 4 ) ] 4 4 3 ⁄ 4 3 ⁄ − 2 𝑑𝑥 = ∫ ( 2 𝑥 + 4 ) 𝑑𝑥 + ∫ ( − 5 2 𝑥 + 10 ) 4 4 3 ⁄ 4 3 ⁄ − 2 𝑑𝑥 = 20
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