The area bounded by the curve x^2=8 y and the straight line x-8 y+2=0 is

Step-by-step solution

Area bounded by curve and line Solving for y in both equations: the parabola becomes y = x^2 8 , and the line becomes y = x+2 8 . The intersection points are found by setting x^2 8 = x+2 8 , yielding x^2 = x+2 or x^2 - x - 2 = 0 . Factoring gives (x-2)(x+1)=0 , so x = -1 and x = 2 are the points of intersection. At x=0 , the line gives y = 1 4 and the parabola gives y=0 , so the line lies above the parabola on the interval [-1,2] . The area is given by the integral of the difference: A = _ -1 ² ( x+2 8 - x^2 8 ) ,