Chapter 9.4, Problem 59E

Evaluate the integral that converge dx (2x- 1)3

What is the total change of f(x), if f'(x) = 3x + 1, over the interval [1, 5]? O -40 O 40 O 42.5 O 45

Find the value of the constant C for which the integral C / (√²+1-1/2+1) 4² :) dx 3x 0 converges. Evaluate the integral for this value of C. C = Value of convergent integral =

Explain why the improper integral (x + 3) sin(x) dx L. (x² + 1)(x² + 4)² is convergent. 8

1

The function values f(x) in the table below is increasing for 0 < x < 12. 0 369 12 f(x) 34 35 37 42 44 (A) Find a right-hand sum to estimate the integral of f(x) dx using all possible intervals in the table above having either Ax = 3 or Ax = 6. Ax = 3, Integral Estimate = Σ Ax = 6, Integral Estimate = Σ (B) Which of the two answers in part (A) is more accurate? Ax = Σ is more accurate (Be sure that you can explain why.) (C) Find a left-hand sum to estimate the integral using Ax = 3. Integral Estimate = Σ

1. Give an example of a function f (x) so that the improper integral " f(x)dx converges. Evaluate the integral. Show your work.

Plz all

- 00 S 2 dx xx² (1 + e²*) (1+e³) -00 X convergent or divergent?