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anonymous
 4 years ago
the functions f and g are given f=sqrt(x) and g = 6x. Let R be the region bounded by the xaxis and the graphs of f and g. Find the area of R
anonymous
 4 years ago
the functions f and g are given f=sqrt(x) and g = 6x. Let R be the region bounded by the xaxis and the graphs of f and g. Find the area of R

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TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.1first step is to get an idea of the shape of the area:dw:1329269119785:dwit looks like we will have to do two separate integrals, because we can see that before the line x=xo we have the area as gf, and after given by fg. xo occurs when the functions intersect, so we can find it by solving\[f(x)=g(x)\]for x. our integral to find R will then be\[R=\int_{0}^{x_o}gfdx+\int_{x_o}^{6}fgdx\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0i found the intersection point between the two curve and its (4,2) so i integrated from 0 to 4 and did f  g why is that wrong?

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.1whoa sorry, misread just\[R=\int_{0}^{x_o}fdx+\int_{x_o}^{6}gdx\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0i get what you are saying their but i am a little confuse to how to know what integral to set up

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0btw thanks for the help

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.1you found that the intersection point is at x=4dw:1329269909705:dwthe first area is under f so it is\[R_1=\int_{0}^{4}fdx\]the second area is under g so it is\[R_2=\int_{4}^{6}gdx\]the total area is then\[R=R_1+R_2=\int_{0}^{4}fdx+\int_{4}^{6}gdx\]

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.1dw:1329270195071:dw

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0I guess its wrong to why is it wrong to integrate for 0 to 6 of f  g...your pic is very good i get that...but i dont get why you can just integrate from 0 to 6

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.1g>f for 0<x<4, so fg would be negative. we want a positive area Imagine there were no g. You can see that R1 would be given by the integral of f from 0 to 4 either way, so excluding g on that interval will give us the right answer fg for 4<x<6 would be the black area on the following graph area:dw:1329270527650:dw so you can see that is not right either.

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.1\[\int_{0}^{4}fdx\]is this area:dw:1329270801204:dw

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.1\[\int_{4}^{6}gdx\]would be thisdw:1329270875759:dw

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.1\[\int_{0}^{4}gfdx\]would be thisdw:1329270925750:dwit is important to think of the shape of each area...

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Ok great explanations that you!!!

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0I will definately be asking more questions ....hope you can help me...lol i am sure you can

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0let me find some more
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