Let us find the area bounded by the curve y=4x−x2 and the lines x=−2 and y=4. Firstly, let us sketch the graph:
It follows that that the area A is:
A=∫−22(4−(4x−x2))dx=∫−22(x2−4x+4)dx=(3x3−2x2+4x)∣−22=38−8+8−(−38−8−8)=38+38+16=2131
Answer: 2131 sq. units
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