The graphs of y = 1 − x^{2} and y = x^{4} − 2x^{2} + 1 intersect at three points. However, the area between the curves can be found by a single integral. Explain why this is so, and write an integral that represents this area.

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Step 1 Given Given curves  y=1-x2 y=x4-2 x2+1Graph :          Step 2 Now we need to find area bounded by curve Area =∫abTop curve-bottom curvedxIn both region Top curve is y=1-x2 and bottom curve is y=x4-2 x2+1So now above formula and find area Area= ∫-111-x2-x4-2 x2+1dx=∫-111-x2-x4+2 x2-1dx=∫-11-x4+x2dx=- x55+x33-11=-1 155+133--1 -155+-133=-15+13-15-13=215--215=215+215=415So we get Area=415By using diagram ,Area of bounded curve is ∫-11Top curve-bottom curvedx=∫-10Top curve-bottom curvedx+∫01Top curve-bottom curvedx ...