1. The problem statement, all variables and given/known data Show that ∫g(x) dx = ∫g(x^2) 2xdx with a=0 and b=1 The followup question asks me to prove that the above integrals are NOT equal, by providing two functions that disprove it (one where the former integral is larger, and one where the latter integral is larger). The last question with this set asks which of the previous two integrals is larger if g(x) is increasing on (0,1)? 2. Relevant equations 3. The attempt at a solution I used g(x)= x and I got u= x^2 du= 2x dx 1 | x^2/2 0 | 1 | u^2/2 0 | x^4/2 1/2 = 1/2 So for the former integral being larger, my example is g(x)= 3x + 6. For the latter integral being larger, my example is g(x)= -(x^2) + 4. For the last question in the set, I have no clue what to do, because only 3x+ 6 is increasing on that interval. In fact, -(x^2) + 4 is decreasing, so I'm stumped. Help please? Thank you.