a)

solve

by substituting

i)

ii)

b)

Can we deduce that

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- Jun 12th 2009, 10:42 PMsimplependulumIndefinite Integral
a)

solve

by substituting

i)

ii)

b)

Can we deduce that - Jun 12th 2009, 11:04 PMmatheagle
I would let or .

If , then

and our integral becomes

.

Next, let giving us

.

From this you can get the arctangent function. - Jun 12th 2009, 11:27 PMMoo
Hello,

1. Substituting is indeed more thorough.

Thus the integral is :

2. Substitute

Thus the integral is :

Now you have to transform with respect to u.

Thus

And the integral is :

And from all this stuff, you can answer question b) (which is not possible with**baldeagle**'s method). - Jun 13th 2009, 05:29 AMJester
One thing to add - be careful with your constants of integration. Clearly

can't be right - it's not true for .