Homework 4, Calculus C

Due Friday August 1st

Exercise 1

Compute antiderivatives for the rational functions g(x) = (9 x^2 - 16 x +4)/(x^3 - 3 x^2 + 2x) and f(x) = -(x^2 - 3 x -7)/(x^3 - 3 x -2)

Exercise 2

Let f(x) = sin(x) cos(x).
a) Compute the indefinite integral of f by substitution.
b) Now compute the same integral as in a) by noting that sin(2x) = 2 sin(x) cos(x)
c) using either a) or b) compute the definite integral of f between 0 and \pi = 3.1415....
d) Apparently, the answers of a) and b) seem to be different, can you explain this?

Exercise 3

Compute the area bounded by the curves y = x^3 and y = x^{1/3} (that is the cubic root of x). Check the signs in your computations and see that in the interval that we are interested, x^3 is smaller than x^{1/3}

Exercise 4

Solve problem 44 in Edwards and Penney section 6.4 (this is not trivial)

Exercise 5

Compute the integrals 2) 14) 28) and 34) in section 9.3 (pp. 524).

Exercise 6

The temperature of a metal rod, 5 m long, is 4 x^2 (in degrees) at a distance x meters from one end of the rod. What is the average temperature of the rod?

Reimundo Heluani

Last modified: Sun Jul 25 11:54:20 EDT 2004