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#1 2006-03-20 01:51:01

AlexPA
Guest

HELP: integrals with constants

Hi,
How do i work out the integral of the following 2:  I dont know how to deal with the constants (C and B)

y = C cos (4x)

y = tan (-Bx)

Thanks alot, Alexroflol

#2 2006-03-20 02:32:12

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: HELP: integrals with constants

The first one is fairly simple.

C is just a constant so we can remove that and put it back in at the end.
We know that d(sin(4x))/dx = 4cos 4x, so naturally that means that 4cos 4x integrates to give sin (4x).

However, we want to integrate cos 4x. This is 4 times smaller than 4cos 4x, so we divide the result of that integral by 4.

∫ cos xdx = C/4 sin 4x + c.

c is an arbitrary constant that must always be included when integrating.

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The second one is harder, because the integral of tan x is less well known. Searching on the internet shows that it is ln |sec x| + c. Now we know this, we can use the same reasoning as in the above example to show that the integral is -1/B * ln|sec x| + c.


Why did the vector cross the road?
It wanted to be normal.

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