EPTA/(x+2) + B/(x-2) + C/x = (x+4)/(x^3-4x), solve for each one and then take the integral of the individual fractions. That's the partial fraction method.
Help my friend since I suck at calc - Page 2
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goldrush
Canada709 Posts
A/(x+2) + B/(x-2) + C/x = (x+4)/(x^3-4x), solve for each one and then take the integral of the individual fractions. That's the partial fraction method. | ||
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Saracen
United States5139 Posts
the derivative of -x^2+4x+5 = ?!? -2x + 4 which just happens to be -2 times (x-2) oh snap function to a power times derivative | ||
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doob10163
6 Posts
On April 02 2008 13:30 Saracen wrote: 11 is just trig sub... it's really straightforward...idk why it's hard? sec(theta) = sqrt(4y^2+1), dy=(sec^2(theta))d(theta)/2 What exactly am I substituting for what here? Thanks for the help, by the way, i really appreciate it. | ||
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goldrush
Canada709 Posts
Since you're not familiar with this stuff, don't try and take shortcuts. Use #17 as an example: Construct a right-angle triangle with a hypotenuse at sqrt2 and the two other sides as x and sqrt(2-x^2). Using pythagoras, you can tell it's right (x^2 + 2 - x^2 = 2, which is the square of the hypotenuse). Alright now... using this triangle, deduce that sin theta = x / sqrt2. Therefore, sqrt 2 * sin theta = x, sqrt 2 cos theta dtheta = dx. You still need to replace sqrt(2-x^2) and x^2 in the original equation though, so... cos theta = sqrt (2- x^2) / sqrt2 sqrt (2 - x^2) = sqrt2 * cos theta original equation of sin theta = x / sqrt2, deduce that x^2 = 2 sin^2 theta. Now, plug it all into the formula: sqrt 2 costheta dtheta / (2 sin^2 theta * sqrt 2 * cos theta) Simplifies oput to 0.5 dtheta/ sin^2 theta. Integrating this turns out to be -0.5 costheta / sintheta. But this is a definite integral and the bounds are also changed becuase of the variable change. Using sintheta = x / sqrt2, plug in 1 and sqrt 2 in the place of x and solve for theta. It turns out to be theta = 90 and 45 degrees. So plug it in... -0.5 [ cos 90 / sin 90 - cos 45 / sin 45] = -0.5 [ 0 / 1 - 1 ] = 0.5 Apologies for any mistakes, it's really late over here. hope this helped.  | ||
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