Integral Calculus Assignment 2541725

1. Find the indefinite integrals of the following functions. Show your work. (a) (8 + 2x x2)1/2 (b) x3/(a8 + x8) (c) [x(xn + an)]1 (d) (1 cos x)/(1 + cos x) 2. Using the identity sec2 x = 1 + tan2 x, find a reduction formula for In = R tann dx, where n is a non-negative integer. Hence write down a general expression for In, distinguishing between n even and n odd. 3. (Problem 4.13 of Textbook)The gamma function (n) is defined for all n > 1 by (n + 1) = Z 1 0 xnexdx. Find a recurrence relation connecting (n + 1)and(n). (a) Deduce the value of (n + 1) when n is a non-negative integer. (b) Given that ( 1 2 ) = p?, find ( 7 2 ). (c) Now, taking the factorial of m for any real m to be defined by m! = (m + 1), evaluate (3 2 )!. 4. (Problem 4.24 of Textbook) The equation of a cardioid in plane polar coordinates is r = a(1 sin ?). (Note, I use the more common notation in physics of r for radial distance and ? for angle as supposed to the book’s ? and Document Preview:

PHYS 320: Mathematical Methods of PhysicsHomework 3Due on Tuesday, February 13th, 8:00PMFebruary 7, 2018Integral Calculus1. Find the inde?nite integrals of the following functions. Show your work.2

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