February 23, 2020, 04:29:39 pm

### AuthorTopic: Unit3 PSMT Help  (Read 107 times)

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#### K.Smithy

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##### Unit3 PSMT Help
« on: February 09, 2020, 03:07:10 pm »
+1
Hi all I hope you're all having a wonderful day.

I just have a question regarding my PSMT. I know what I need to do, but in some sections I am unsure of how to do it.

Our task is to design a pendant and calculate the area and volume of the pendant using calculus.
My design is:

(if you're curious, it is a very ugly version of the golden snitch from Harry Potter )

I know I need to integrate the functions and calculate the area between curves for some of them, and others (the two semi circles for example) I need to integrate and calculate the area between curve and the x-axis...
... actually, for the two semi circles, would I be able to do area between the curve for them as well?
Also, was it a good idea to do two semi circles instead of one circle? The reason I decided to do semi circles was because you can't (from what I'm aware) integrate a circle (is it because it is a relation not a function??)... I want to show, as much as possible, my ability to perform processes with calculus - rather than just using normal mensuration formulas.

Anywho, I digress... what I am confused about is how to calculate the area of the the wings of my snitch... The top of the wing goes further than the bottom of the wing, which means the semi circle gets in the way..
My thought is... integrating between where the two functions meet (at x = -30 and 30) and going to where the bottom function meets the circle (x = -10 and 10) and then from there, integrating the exponential and the semi circle (from x = -10 and 10, to x = -9.794 and 9.794)...
If that doesn't make any sense I'll try to re-word my question

Any help would be greatly appreciated thanks everyone!
QCE 2020: Physics || Psychology || Biology || Mathematical Methods || General English || Study of Religion

#### Bri MT

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##### Re: Unit3 PSMT Help
« Reply #1 on: February 09, 2020, 07:20:12 pm »
+1

Hi! Hope you've had a wonderful day!

You're on the right track in terms of thinking about needing to consider the intersections when you're integrating. Remember that to find the area between two curves you want to take the absolute value of  F(x)-G(x) where g(x) is the function closer to the x-axis. I've attached a picture which should help you visualise this. (You haven't mentioned the intersection between the semicircle and the quadratic but you do need to consider that too)

Between 10 and 9.794 you do need to consider the area added by the semicircle, but the process for finding the area between the exponential and linear function doesn't change.

Because you need to integrate sections of the positive semicircle function, it might demonstrate more mathematical understanding to use geometry for the lower half of the circle; however, I'm not familiar with qce maths assessment so please don't blindly follow me on this.

Two semicircles instead of one circle was definitely a good idea unless polar co-ordinates and using those for integration is covered in methods (which I doubt)

Hope this helps!

Edit: fixed typo
« Last Edit: February 09, 2020, 09:12:17 pm by Bri MT »

#### K.Smithy

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##### Re: Unit3 PSMT Help
« Reply #2 on: February 09, 2020, 07:26:17 pm »
0
-snip-

Awesome, thank you so much Bri! You are a lifesaver!
QCE 2020: Physics || Psychology || Biology || Mathematical Methods || General English || Study of Religion