- #1

Ahlahn

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Below are three questions relating to the integration between curves that have been bugging me for some time now. I know how to integrate between curves. I know how to integrate between x and y, but when given equations like the ones below I am lost as to how to figure out 2 things

1. What the graphs look like(so I know which one is left/right, top/bottom)

2. The points of intersection(to figure out the interval [a,b])

You don’t have to answer all of my questions(Though that would be Awesome), but it would really help if you could point me in the right direction by telling me what I’m doing wrong so I won’t keep running into the same problems again. Thanks so much!

__Question 1__**.**

Find the area of the region enclosed by the semicubical parabola y2 = x3 and the line x = 3

Find the area of the region enclosed by the semicubical parabola y2 = x3 and the line x = 3

I am having a lot of trouble with questions like this one. I am assuming that the question is asking me to integrate along the y-axis between the curves x=y^2/3 and x=3, but what is the interval? How can I find the interval when given functions like these? What am I doing wrong?

**Question 2**

**Sketch the region enclosed by the curves and compute its area as an integral along the x- or y-axis.**

x = y3 - 18y, y + 7x = 0

x = y3 - 18y, y + 7x = 0

I rewrote it as ...X = y^3 – 18y and x = -(1/7)y

Like the previous question, I have trouble figuring out how the graphs look like, which one lies on top or side- so I am clueless as to whether I should integrate along the x or y…

Question 3

Question 3

**Find the area enclosed by the curves listed below as a function of c.**

y = c - x^2

y = x^2 - c

y = c - x^2

y = x^2 - c

Okay so I plugged a random constant for c and found that the function y = c-x^2 lies on top, therefore we are integrating along the x axis. I then tried looking for the points of intersection, and failed. How can I find the interval if c is unknown?! O_O

Again, thanks everyone in advance!