Find the area of the region enclosed by the curves y2 - 2x = 7 and x - y = 4. Th

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Putting y=3x+4 in y=x^2 + 4 to find intersection => x^2 + 4 - 3x - 4 = 0 => x=3,0 Hence y = 13,4 Points are (3,13) and (0,4) Area bounded by curves is the area under the line minus the area under the curve from (0,4) to (3,13). This is because the line lies over the curve in this interval area under line = integral(3x+4) from 3 to 0 = (3x^2/2 + 4x) from 3 to 0 = 25.5 area under curve = integral(x^2 + 4) from 3 to 0 = (x^3/3 + 4x) from 3 to 0 = 21 Area bounded by the curves = 25.5 -21 = 4.5 units

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