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anonymous
 one year ago
Find the area of the region bounded by the curves y = x^2 − 1 and y = sin(x). Give your answer correct to 2 decimal places.
anonymous
 one year ago
Find the area of the region bounded by the curves y = x^2 − 1 and y = sin(x). Give your answer correct to 2 decimal places.

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0not sure what to do about the graph being partially in the negative quadrants

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i found the endpoints of intersection at 0.636733 and 1.40962 not sure where to go on from there

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@ganeshie8 @dan815 @Michele_Laino @pooja195 @Kainui

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0do i have to integrate with respect to the yaxis ?

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.2hope this helps you

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i had already graphed it :(

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.2cool found where they intersect?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yep at x = 0.636733 and 1.40962

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0not sure what to do next ...

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.2well, next integrate :p i'd be sure to keep the +ve and ve signs in order so you might wish to do 2 integrations. they cross at x = 0. so integrate x = 0.636733 to 0, and x = 0 to 1.40962 all in dx you can do dy if you want but you are creating a whole load of problems for yourself such as having to integrate arcsin

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0wouldn't the fact that some of the graph is on the negative quadrants give me a wrong answer

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.2yep, that's exactly what you have to look out for i'll try draw something

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.2dw:1438890387798:dw

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.2it's a real drag but you will need a way to keep the sign consistent, the areas under the curve will come out as negative. i think you already know that. so you just have to deal with it.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0well thats what i don't know how to do

freckles
 one year ago
Best ResponseYou've already chosen the best response.1should be able to do integrate topbottom

freckles
 one year ago
Best ResponseYou've already chosen the best response.1y=sin(x) is always above y=x^21 on the given interval

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0wouldn't the integration include everything between the function and the red line too? dw:1438891297985:dw

freckles
 one year ago
Best ResponseYou've already chosen the best response.1so you want to include more area than shown?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1dw:1438891485605:dw you want this area

freckles
 one year ago
Best ResponseYou've already chosen the best response.1dw:1438891497073:dwnot this

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0no, im just saying that if you find the integral of the top area it will find this area dw:1438891538121:dw which includes some area that i don't want

freckles
 one year ago
Best ResponseYou've already chosen the best response.1so you aren't convinced the area is given by: the integration of the (topbottom) on the given interval? I may be able to help you understand that if that is what you don't understand

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0im just not clear on how you would find the area of the top precisely thats all

freckles
 one year ago
Best ResponseYou've already chosen the best response.1dw:1438891880460:dw

freckles
 one year ago
Best ResponseYou've already chosen the best response.1let me just start with this piece this is going to give you overlap

freckles
 one year ago
Best ResponseYou've already chosen the best response.1you want to subract out that one part

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.2i am such a moron shift the whole thing up by 1 integrating between \(y = x^2 1\) and \(y=sin x\), "magnitudewise", is same as integrating between \(y = x^2\) and \(y = sin x + 1\) you will have same x intercepts too

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0you can do that !!!!!

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.2ask @freckles sorry @freckles i had one of those "duh" moments......

freckles
 one year ago
Best ResponseYou've already chosen the best response.1yeah and we should wind up with \[\int\limits_{0.637}^{1.141 }(\text{ top }  \text{ bottom }) dx \\ \int\limits_{0.637}^{1.141 }(\sin(x)  (x^21)) dx \\ \] but trying to think how to explain this in pieces... \[\int\limits_0^{1.41 } \sin(x)dx\int\limits_c^{1.41} (x^21) dx\int\limits_0^c (x^21)\int\limits_{.637}^0 (x^21)dx\int\limits_{.637}^{0} \sin(x) dx \\ \text{ as we see this gives us } \\ \int\limits_{.637}^{1.41} \sin(x) dx\int\limits_{.637}^{1.141}(x^21) dx \\ \text{ which can be written the way \above } \\ \int\limits_{.637}^{1.41} (\sin(x)(x^21) )dx\] it is hard for me though to draw some of this overlapping stuff

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay so then it would be \[\int\limits_{.636}^{1.409}\sin(x) +1  x^2\] right?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1yes exactly you just do top  bottom

freckles
 one year ago
Best ResponseYou've already chosen the best response.1shouldn't be a negative number

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0for got the +1 1.6702

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thank you very much :D
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