Chapter 6, Problem 16RE

What would be an example of a function that is not integrable on [2, 10] and why is it not integrable?

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

Find all the analytic functions for ReZ=Im f(z)

Questions: A) find the indefinite integral of the function y = 3t^2 + 2e^3t + 1/t + 2cos3t?B) calculate the definite integral: (this is an integral operator, with a 1 at the bottom and 2 at the top of the integral operator) 1int2 3t^2 + 2e^3t + 1/t + 2cos3t dt ?

f:[0,1] -> [0,1] such that f(x)=x^2 has two fixed points. Is this true?

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.

Find f if ∇f = 4xy i + (2x^2 + 8y) j

Use the Fundamental Theorem to evaluate the definite integral exactly. 1 (»6 + y® )dy Enter the exact answer. 1 + y* )dy = ,8'