Area Within a Curve
Hey everybody, newbie here, looking for some quick help. I promised a good friend of mine help with her calculus homework, but I've gotten rusty, and only have a fleeting glimpse of what I should be doing. PLEASE HELP
Here's the functions, of which I've got to find the area within the curve.
y=x^3 - 5x + 2
The graph kinda looks like a horizontal parabola & a vertical snake...
The relevant points of intersection I've found are:
(.12666695, 2.0567), (2,0), & (.69576957, -1.1420)
Of course the x-values are the only ones needed.
the upper limits for Int1 are .12666695, and .69576957
The upper limts for Int2 are .69576957, and 2
This is where I am stuck.
Do I plug them into Sqrt(2-x) - ((x^3) - 5x + 2), or have I missed a step?
It is beyond late right now, so if I could get some assistance while I sleep, I'll be eternally grateful.
This is an irritating problem. Who came up with this anyway?
Originally Posted by Jughead5267
Notice that there are actually 3 integrals you need to do:
Integrate from x = 0.126666947 to x = 0.695769572
Integrate from x = 0.695769572 to x = 1.978833423
Integrate from x = 1.978833423 to x = 2
(See the two graphs below. The second is a blown up view of the region around x = 2.)
When you find the area you take the difference between the two functions that are creating the area. So