I am new to the forums and would appreciate a little help on this problem
I have a homework problem that states the following:
You are not allowed to use a calculator. Just use logic. Show all work.
Using the properties of integrals prove that : ∫ √((x^4)+1)dx >= 26/3
Definite integral from 1 to 3 (3 being upper limit, 1 being lower)
well what I did was make a U-Substitution
u = (x^4) + 1 ----> dx = du/4(x^3)
giving me (1/4x^3) ∫ u^(1/2) du
but from there i am lost. Using my ti-83 i found that the definite integral from 1 to 3 √((x^4)+1)dx = 8.98.... , which is greater than 26/3
I just dont know how I am messing up, after integrating this I get: (u^(3/2)) / (6(x^3))
but when i do F(b) - F(a) I am not getting the answer 8.98.. and do not know how to do this without my calculator
I wouldn't recommend trying to compute the exact value of the integral. It involves elliptic functions.
Here's the beauty of inequalities: you have loads of freedom. You can throw away stuff left and right, simplify, and yet keep the inequality. If you follow the train of reasoning I gave in Post #2, what can you do with the integral to the right of my inequality?