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# FP3 Rectangular approximation to series watch

1. So I have to find the upper and lowers bounds for the sum of sinr where r is in degrees between 1 and 89, leaving the bounds to 4.s.f

I did this but evidently that is incorrect ...so how do I do this?
2. (Original post by Mathematicus65)
So I have to find the upper and lowers bounds for the sum of sinr where r is in degrees between 1 and 89, leaving the bounds to 4.s.f

I did this but evidently that is incorrect ...so how do I do this?
firstly draw a picture
secondly do the integration in radians
3. (Original post by TeeEm)
firstly draw a picture
secondly do the integration in radians
I've sketched it, and evidently sinx is an increasing function between x =1 degree and x =89 degree.

And I integrated in radians also and still got the incorrect answer, but the question says that x is specifically to be in degrees?
4. you seem to have changed the limits from "1 to 89" to "0 to 89" near the start
5. (Original post by Mathematicus65)
And I integrated in radians also and still got the incorrect answer, but the question says that x is specifically to be in degrees?
is only true if you work in radians.

So, if x is in degrees, you have to convert it to radians? What's your multiplying factor?
6. (Original post by Mathematcius65)
..
Note that your conversion to radians needs to happen inside the integral, not by changing the limits. The limits need to match the limits for the sum, so they are actually correct as they stand.
7. (Original post by DFranklin)
Note that your conversion to radians needs to happen inside the integral, not by changing the limits. The limits need to match the limits for the sum, so they are actually correct as they stand.
How do you mean inside?
8. (Original post by Mathematicus65)
How do you mean inside?
The correct integral is

That is, the issue is that in normal calculus, sin x means the sin of x measured in radians. But here x is measured in degrees. So you need to scale x from radians to degrees.

K
(Note this is a bit vague because I don't want to just give you the answer).

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