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 April 15th, 2012, 12:13 AM #1 Newbie   Joined: Apr 2012 Posts: 5 Thanks: 0 Evaluate Integrals Evaluate the following Integrals over the given intervals: A) (4/2x-1) - (3/x+4) over [1,3] B) cosh 3x-sinh4x over [0,Ln2]
 April 15th, 2012, 07:59 AM #2 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,879 Thanks: 1087 Math Focus: Elementary mathematics and beyond Re: Evaluate Integrals $\int_1^3\frac{4}{2x\,-\,1}\,-\,\frac{3}{x\,+\,4}\,dx\,=\,$$2\ln(2x\,-\,1)\,-\,3\ln(x\,+\,4)$$\line(0,40)_1^3\,=\,\ln$$\frac{31 25}{343}$$$ $\int_0^{\small{\ln(2)}}\cosh(3x)\,-\,\sinh(4x)\,dx\,=\,\int_0^{\small{\ln(2)}}\frac{e ^{6x}\,+\,1}{2e^{3x}}\,-\,\frac{e^{8x}\,-\,1}{2e^{4x}}\,dx \\ =\,\int_0^{\small{\ln(2)}}\frac{1}{2}e^{3x}\,+\,\f rac{1}{2}e^{-3x}\,-\,\frac{1}{2}e^{4x}\,+\,\frac{1}{2}e^{-4x}\,dx \\ =\,$$\frac{1}{6}e^{3x}\,-\,\frac{1}{6}e^{-3x}\,-\,\frac{1}{8}e^{4x}\,-\,\frac{1}{8}e^{-4x}$$\line(0,40)^{\ln(2)}_0\,=\,\frac{-57}{128}$

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