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Integral Calculus

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24 Oct 2007 22:59:38 IST

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300

integration offfffffffffffff

None

^{of odd powers of sin and cos}

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Aditya Arora

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Joined: 3 Dec 2006

Posts: 1043

24 Oct 2007 23:06:15 IST

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Well, as you go higher, it would be difficult to solve indefinite integrals. but definite integrals can be solved easily.

For eg:

_{[ ]}^{[ ]} sin¹⁵x dx

_{[ ]}^{[ ]} sin¹⁴x*sinxdx

_{[ ]}^{[ ]} (1-cos²x)⁷ sinxdx

Put t = cosx ......................... Eq. 1

differentiate both sides

dt = -sinxdx

So,

_{[ ]}^{[ ]} -(1-t²)⁷ dt

Now you will have to open the polynomial and then solve it

ram kumar

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Joined: 14 Aug 2007

Posts: 407

25 Oct 2007 21:58:19 IST

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hints to evaluate

(sinx)^m*(cosx)^ndx where m and n are natural numbers

(i) if m is odd put cosx = t
(ii) if n is odd put sinx=t
(iii)if both m and n are odd you can substitute either sinx=t or cosx=t
(iv) if both m and n are even use trigonmetric identities
(v) if m and n are rational numbers and (m+n-2)/2 is a negative integer , then substitute cotx=t or tanx=t

i hope you are clear with my reply!!

pradnya pednekar

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Joined: 24 Oct 2007

Posts: 8

26 Oct 2007 20:54:03 IST

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_{[ ]}

^{[ ]} _x²--1

_{------------------}

^_x4+3x^2₊₁

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