|
|
|
STEP II 1997 question 8 solutionTSR Wiki > Study Help > Subjects and Revision > Mathematics > STEP > STEP II 1997 question 8 solution I'm not sure what the "standard explanation" is here. I think Siklos says you just need to draw a couple of vague wiggles and say the integral is the area under the curve. More formally, if f,g are cts, consider the integral of f-g, apply the fundamental theorem of calculus and the mean value theorem to show that If p > q and x>=1 then If p > q and 0 <= x <1 then Doing the same trick on the inequality we've just found gives us
If x > 0, dividing by x gives the desired result, while if x=0 the result is obviously true. Solution by DFranklin |
|
|||||||||||||||
![\displaystyle \int_a^b (f-g)(x) dx = (b-a)[f(c)-g(c)]](http://www.thestudentroom.co.uk/latexrender/pictures/2d/2d2b3955f9309ded1fa64c9324f2a584.png "\displaystyle \int_a^b (f-g)(x) dx = (b-a)[f(c)-g(c)]")
