Chapter 6, Problem 21RE

3

What is meant by indeterminate integral

I) Í dx/ (x² + 4x + 3) find integral

Write some important things about integral calculus

How do you integrate z/(z+2) in terms of z?

Use the Fundamental Theorem of Calculus to give alternative proofs of the integration facts shown in Exercises 72–76. You may assume that all functions here are integrable. 72. cdx = c(b – a) 73. x dx = 1 x² dx (b³ – a®) kf (x) dx = k | f(x) dx 74. 75. | (f(«) +g(x)) dx = | f(x) dx + g(x) dx 76.

z is a complex variable z=x+iyShow that f(z)=((z^2)+1)/((z^2)-3z+2) is continuous for all z outside |z|=2

28. Consider the integral in Example 1: x²e»+ Show that the integrand can be expressed as a product g(x)h(y)k(z). Then verify the equation in Exercise 27 by computing the product of integrals on the right-hand side and showing it equals the result obtained in the example.

Let x, y be real numbers such that xy=1x and x≠y. Prove that x^2+y^2≥2\sqrt{2}|x−y|.