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anonymous
 one year ago
Evaluate the integral by interpreting it in terms of areas.
S^0 on the bottom 6 (5+root36x^2)dx
I have no idea how to work this problem out, please help!
anonymous
 one year ago
Evaluate the integral by interpreting it in terms of areas. S^0 on the bottom 6 (5+root36x^2)dx I have no idea how to work this problem out, please help!

This Question is Closed

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.5Take a good look at the integrand, does it look familiar to you ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the 6 is on the bottom of the integral, um no not really

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.5like this ?\[\large \int\limits_{6}^0 \color{blue}{5+\sqrt{36x^2}}\, dx\]

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.5May be rearrange the integrand a bit \[\large y=\color{blue}{5+\sqrt{36x^2}}\] \[\large (y\color{blue}{5})^2=(\color{blue}{\sqrt{36x^2}})^2\] \[\large \color{blue}{x^2}+(y\color{blue}{5})^2=\color{blue}{36}\] what about now ? seen this before ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0it has to do with circles right?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.5dw:1436074459700:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.5look at only the top half, because the original function is \(y=5+\sqrt{36x^2}\), which represents only the upper half of circle.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.5you need to find the area under that curve between x=6 and x=0

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.5dw:1436074742051:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.5thats the area the given integral represents see if you can work it

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0would my answer be 36pi/2? Im not really sure what Im supposed to do, this is the firts problem i have that is like this

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.5how did you get 36pi/2 ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.01/2pir^2=1/2pi6^2=36pi/2 and then i did it another way and got 30

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.5nope, notice that the area is made up of a "quarter circle" and a "rectangle" : dw:1436075697415:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.5find area of quarter circle, find area of rectangle add them up

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay, what do i do (5+root36x^2)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0would my answer be 6+9pi? @ganeshie8

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.5whats the area of rectangle ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.5dw:1436076828225:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0is that a 5? so it would be 25

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.5careful, you need to use area of rectangle formula not area of square

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.5Yes, save that, next find the area of quarter circle

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.5Looks good! add them up

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.5\[\large \int\limits_{6}^0 \color{blue}{5+\sqrt{36x^2}}\, dx~~=6\times 5+\dfrac{\pi\times 6^2}{4} = 30+9\pi\]
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