ECON 1000 Midterm: ECON 1000 Kennesaw State ECON1000 Fall2016 Exam1A
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Part a: (20 points) (a) find the partial fraction expansion of (b) calculate the integral. Note: the rst part of this problem was designed to help you do the second part. If you did the rst part incorrectly, you will not get partial credit for correctly using the wrong partial fraction expansion to nd the integral. Solution: (a) x3 x = (x + 1)x(x 1). C x 1 x3 x x + 1. Putting the right hand side on a common denominator we get. 2 ln|x + 1| = lnp|x + 1| x. 1 dx = ln|x| = ln(1/|x|) dx = ln|x 1| = lnp|x 1| X2 1 dx = lnp|x + 1| + ln(1/|x|) + lnp|x 1| + c. Solution: a right triangle with sides 2 and x will have hyppotenuse x2 + 4. Let be the angle opposite the side with length x. Then we have x = 2 tan dx = 2 sec2 d .
