Question #183898

Find the area bounded by the curve x²=y+2 and the line x+y=0.

Expert's answer

Let us find the x points of intersection of two graphs "y_1(x) = x^2 - 2" and "y_2(x) = - x" by solving corresponding quadratic equation "x^2 - 2 = -x". It has roots "x = -2 , x = 1".

Hence, the area between two curves is:

"S = \\int_{-2}^1 (-x - (x^2 - 2 )) d x = (-\\frac{x^2}{2} - \\frac{x^3}{3} + 2 x)|_{-2}^1 = \\frac{9}{2}".

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