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How would i go about solving with trig sub?
Hi, ive been stumped by this integral as it does not contain a root, can anyone help?
- Engr. RonaldLv 71 month ago
=- 1/3x^3 + 9x + C answer//
Let x=3sinA, then dx=3cosAdA
I=27[S cosAdA-S sin^2(A)d(sinA)]
If you want the result in terms of x, you
should integrate directly with respect
to x getting I=9x-(x^3)/3+C.
- 1 month ago
Hi, I'm sure you know how to solve it by the easiest method, although it is likely that you were asked to solve it with trig sub.
So to solve it by trig sub in this case you can use a mathematical artifice. you artificially add a root and thus use trig sub normally.
- alexLv 71 month ago
∫ax^n dx = (a/(n+1))x^(n+1)+C , where n≠ -1
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So easy it's difficult!
Integral of -x^2 dx is -x^3/3,
integral of 9 dx is 9x,
answer to your problem is 9x - (1/3)x^3 + C.
Don't do "trig sub" !!!
You would directly integrate this. You would not use trig sub to do this. Although you can, you will just really really overcomplicate matters.
- L. E. GantLv 71 month ago
= - ∫(x^2-9) dx
= -∫x^2dx + ∫9 dx
= -x^3/3 + 9x +C
stop looking for complications!
- KrishnamurthyLv 71 month ago
integral(-x^2 + 9) dx = 9 x - x^3/3 + constant