Math Is Fun Forum

FP2Student

Guest

Finding Bounds for Series using Integrals.

Hey, this is the question I have been posed with:

Find the upper and lower bounds of this summation:

So basically that is:

sin 1 + sin 2 + sin 3 + ... + sin 88 + sin 89.

We've been taught to use integrals for finding the upper and lower bounds.

The upper bound will be the integration:

Is that right?

And then the lower bound will be:

However, the answer should be in the 30 region. Those integrals don't give me the right answer. What have I done wrong?

Please help, thank you in advance.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Finding Bounds for Series using Integrals.

Hi FP2Student;

I think you have the wrong estimate for the sum:

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

FP2Student

Guest

Re: Finding Bounds for Series using Integrals.

Is that in radians?

Because in degrees, it is actually 56.79432507...

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Finding Bounds for Series using Integrals.

Hi;

Yes that is in radians.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

FP2Student

Guest

Re: Finding Bounds for Series using Integrals.

Ah, okay then.

How would you work it out in degrees then?

The integrals don't seem to give the right answer.

Am I right in thinking that

is -cos90+cos 1?

Because that gives an answer of 0.99987695 which doesn't fit with the value of 56.79432507... I have.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Finding Bounds for Series using Integrals.

Hi FP2Student;

The formulas for calculus are made to work in radians not degrees. You can try converting those radian values to degrees but I don't think that is correct.

Over here they are having an interesting discussion as to why radians and not degrees are preferred.

https://nrich.maths.org/discus/messages … 1073606796

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.