Answer to Question #176649 in Calculus for Joshua

Question #176649

Find the area bounded by the curve y=4x-x^2 and the lines x=-2 and y=4.


1
Expert's answer
2021-03-30T16:14:03-0400

Let us find the area bounded by the curve y=4xx2y=4x-x^2 and the lines x=2x=-2 and y=4y=4. Firstly, let us sketch the graph:





It follows that that the area AA is:

A=22(4(4xx2))dx=22(x24x+4)dx=(x332x2+4x)22=838+8(8388)=83+83+16=2113A=\int_{-2}^2(4-(4x-x^2))dx=\int_{-2}^2(x^2-4x+4)dx=(\frac{x^3}{3}-2x^2+4x)|_{-2}^2= \frac{8}{3}-8+8-(-\frac{8}{3}-8-8)=\frac{8}{3}+\frac{8}{3}+16=21\frac{1}{3}


Answer: 211321\frac{1}{3} sq. units


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