Mean Value Theorem for integrals w/ log

An arched shaped monument is 570 ft high and has a 600 ft base. It can be modeled by the function where the base of the arch is[-300,300] and x and y are measured in feet. Find the average height of the arch above the ground.

I was able to do this but it took a while. What is the best way to to do this so I dont have to enter too many buttons on my calculator which personally increases my rate of error.

My questions: 1. Can I use **ln** on the integrand and what would it look like? 2. How do I deal with symmety for a LN()?

factor out 285 and distribute the minus sign

Can I use a Natral Log? and does it look like this???

Specifically, I want to know do I use LN on the **factored** out numbers and the **avgvalue**?

If all is well then My next step would be to split up the intrgrand and check for symmetry. If I didnt previously apply the Ln, then all of the integrand was an even functon. It appers that is an even function but what about LN(x)

ln(-x)= no bueno

Re: Mean Value Theorem for integrals w/ log

Quote:

Originally Posted by

**delgeezee** An arched shaped monument is 570 ft high and has a 600 ft base. It can be modeled by the function

where the base of the arch is[-300,300] and x and y are measured in feet. Find the average height of the arch above the ground.

I was able to do this but it took a while. What is the best way to to do this so I dont have to enter too many buttons on my calculator which personally increases my rate of error.

My questions: 1. Can I use

**ln** on the integrand and what would it look like? 2. How do I deal with symmety for a LN()?

factor out 285 and distribute the minus sign

Can I use a Natral Log? and does it look like this???

Specifically, I want to know do I use LN on the

**factored** out numbers and the

**avgvalue**?

If all is well then My next step would be to split up the intrgrand and check for symmetry. If I didnt previously apply the Ln, then all of the integrand was an even functon. It appers that

is an even function but what about LN(x)

ln(-x)= no bueno

note that the antiderivative of is ... it does not involve a log

let

also note that you may take advantage of symmetry ...

Re: Mean Value Theorem for integrals w/ log

Quote:

Originally Posted by

**delgeezee** An arched shaped monument is 570 ft high and has a 600 ft base. It can be modeled by the function

where the base of the arch is[-300,300] and x and y are measured in feet. Find the average height of the arch above the ground.

I was able to do this but it took a while. What is the best way to to do this so I dont have to enter too many buttons on my calculator which personally increases my rate of error.

My questions: 1. Can I use

**ln** on the integrand and what would it look like? 2. How do I deal with symmety for a LN()?

factor out 285 and distribute the minus sign

Can I use a Natral Log? and does it look like this???

No. ln(a+ b) is NOT equal to ln(a)+ ln(b).

Quote:

Specifically, I want to know do I use LN on the **factored** out numbers and the **avgvalue**?

I don't see why you would want to. The logarithm is not relevant. You want to integrate

all of which are very easy integrals.

Quote:

If all is well then My next step would be to split up the intrgrand and check for symmetry. If I didnt previously apply the Ln, then all of the integrand was an even functon. It appers that

is an even function but what about LN(x)

ln(-x)= no bueno