Using double integration, find the area for x > 0 that is enclosed by the y - ax is, the curve y = 9 – x 2 and the line y = 8x

Question

Using double integration, find the area for x > 0 that is enclosed by the y-axis,the curve y = –x2and the line y = 8x

 

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Answer 1

y=-x^2 is a downward opening parabola with vertex = max = the origin

y=8x is a steeply sloped upward straight line

y axis is the vertical line x=0

area between them is bounded on the left and right by the points where 8x =-x^2

x=-8 and 0

y=-64 and 0

they are the limits of integration,

area enclosed is below the x axis and to the left of the y axis is 108.333

the y axis is redundant to this problem

unless you meant y=9-x^2, then a different result