Evaluate the definite integral:
(1)∫(9) [ (4x^2+3) / (√x) ] dx
(the integral is from 1 to 9)
I have been trying to do this problem for hours and I have had no success, please help! Explain any work if possible, thank you!
by 
Anonymous
ANSWERS: 1
-
I would try u=sqrt(x)=x^0.5 du/dx = 0.5 x^-0.5 so 2du/dx is part of your question already. You have [4x^2 + 3]/sqrt(x) which is [4x^2 + 3] * 2 * du/dx = [4 u^4 + 3 ] * 2 * du /dx Using the chain rule this becomes: = Integral u(0) to u(9) of [ 4 u^4 + 3 ] * 2 du which is a simple one. It's clear this is the way we were intended to do it because u(9) is a nice round number. If in doubt you can always set u to each part of the integrand and use the chain rule many times to see if any of the u make the integral simpler. If not, look for integration by parts: try to split the integral into a'*b where a*b and a*b' are both easier to integrate.
RELATED QUESTIONS
Copyright 2023, Wired Ivy, LLC