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Calculus (Area Between Curves)

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Find the area of the region bounded by the curves y^2=x, y-4=x, y=-2 and y=1
(Hint: You'll definitely have to sketch this one on paper first.) You get:
a.) 27/2
b.) 22/3
c.) 33/2
d.) 34/3
e.) 14

  • Calculus (Area Between Curves) -

    Since y^2 = x is not even defined left of the y-axis, the region is

    x<3: a triangle bounded by y=x+4, x=-3, y=-2
    area = 3*3/2 = 9/2

    -3<x<0: a rectangle, area 3*3=9

    0<=x<=1: a curved triangular area
    area = Int(1-√x)dx [0,1]
    = (x - 2/3 x√x)[0,1]
    = (1 - 2/3) = 1/3

    Total: 9/2 + 9 + 1/3 = 14 - 1/6

    Almost (e), but not quite. Typo somewhere?

  • Calculus (Area Between Curves) -

    find the definite integral y^2 - y + 4 evaluated from -2 to 1. I go 16.5 sq units Choice c

  • Calculus (Area Between Curves) -

    33/2 is correct.

  • Calculus (Area Between Curves) -

    Thank you Nade for making this correction! I went back and graphed the functions with pencil to see if I could figure a rough estimate for the area. I found that these function make an odd trapezoid shape. The area of the solid trapezoid portion of the graph is 15 and then there is a small portion on the other side of the y-axis. So, I, too, figured that 33/2 would be the most reasonable answer. Thank you both!

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