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Integration question

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1. Integration question
This is the info we are meant to use;

and that k(x) has a local max at x = 3 and local min at x = 7.

Use all that to find area below the graph of

and above the x axis. Give your answer to five sig figures.

I'm not spotting whatever it is that I'm supposed to notice. I know that you're supposed to deduce the limits somehow to get an actual value to the integration but even then don't know how to make that deduction just yet but first of all, no idea how to integrate that. Just hoping someone could give me a starting point.
Last edited by Preeka; 29-07-2012 at 20:49.
2. Re: Integration question
For the limits first - take a look at . Where is this function positive? Where is it negative?

Now note . Look at the function - where is that positive? Where is it negative?

The area above the x-axis is where y is positive. As the product of two functions, we can see y is positive only where and are both positive, or and are both negative. So what range is this?
3. Re: Integration question
(Original post by Preeka)
This is the info we are meant to use;

and that k(x) has a local max at x = 3 and local min at x = 7.

Use all that to find area below the graph of

and above the x axis. Give your answer to five sig figures.

I'm not spotting whatever it is that I'm supposed to notice. I know that you're supposed to deduce the limits somehow to get an actual value to the integration but even then don't know how to make that deduction just yet but first of all, no idea how to integrate that. Just hoping someone could give me a starting point.
For integration of y
Consider that

Integrate by part twice
4. Re: Integration question
(Original post by ztibor)
For integration of y
Consider that

Integrate by part twice
Have you tried this? I don't think there's a way to actually integrate this without resorting to numerical methods

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Last updated: July 31, 2012
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