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Chipset3600
Member
- Feb 14, 2012
- 79
Hello MHB, how can i solve this without use integration technniques...
[TEX]\int tan(t)sec^3(t)dt[/TEX]
[TEX]\int tan(t)sec^3(t)dt[/TEX]
How do you mean "without using integration techniques"? Surely you need integration techniques to solve an integral? Also what have you tried?Hello MHB, how can i solve this without use integration technniques...
[TEX]\int tan(t)sec^3(t)dt[/TEX]
I mean without: substitution, integration by parts...How do you mean "without using integration techniques"? Surely you need integration techniques to solve an integral? Also what have you tried?
Hint: Let $u = \sec(t) = \frac{1}{\cos(t)}$
How can i solve this without use integration technniques?
. . [TEX]\int \tan\theta \sec^3\!\theta\,d\theta[/TEX]
[TEX]\int tan(t).sec^3(t)dt = \int sec^2(t).sec(t).tan(t)dt[/TEX]Hello, Chipset3600!
Well, maybe you can see all this?
If we have: .[tex]f(x) \:=\:\tfrac{1}{3}\sec^3\!\theta + C[/tex]
Then: .[tex]f'(x) \:=\:\tfrac{1}{3}\cdot 3\sec^2\!\theta\cdot\sec\theta\tan\theta + 0 \;=\;\tan\theta\sec^3\!\theta [/tex]