Find the area of the region bounded by y = x2 and y = 2x – x2

Question

Find the area of the region bounded by y = x2 and y = 2x &#8211; x2

Suresh Chand · Accepted Answer

Solution: First we will sketch two curves in figure. The limit of integration are found by solving y = 2x - x2 and  y = x2 simultaneously for x. or, x2 = 2x - x2 or, 2x2 - 2x = 0 or, x = 0,1 The region runs from x = -1 and x =2. the limit of integration are n = -1, b = 2. The area between the curves is (A = int_{a}^{b} [f(x) - g(x)]dx) ( = int_{0}^{1} [2x - x^2 - x^2]dx) ( = int_{0}^{1} [2x - 2x^2]dx) (=left [ frac{2x^2}{2} - frac{2x^3}{3} right ]_{0}^{1}) (=left [ x^2 - frac{2x^3}{3} right ]_{0}^{1}) (=1 - frac{2}{3}) (= frac{1}{3})

Find the area of the region bounded by y = x² and y = 2x – x²

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Find the area of the region bounded by y = x2 and y = 2x – x2

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Find the area of the region bounded by y = x² and y = 2x – x²