What are the guaranteed values of c for the Mean Value Theorem for Integrals?

[kings13]

Homework Statement

Find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the given interval.

Homework Equations

f(x)=3cos(x), [-pi/4, pi/4]

The Attempt at a Solution

well i do f(b)-f(a)/b-a and get zero but that's not the answer whenever i try it..

 

[Strants]

What does the Mean Value Theorem for Integrals say? (It's more specific than just the Mean Value Theorem).

 

[kings13]

What does the Mean Value Theorem for Integrals say? (It's more specific than just the Mean Value Theorem).

the average area under the graph?

1/b-a times f(c) right? but how to put numbers into that

 

[Mark44]

What are a and b? What is f in this problem? What is the value of the integral, namely this one?
\int_{-\pi/4}^{\pi/4} 3 cos(x)dx

 

[kings13]

What are a and b? What is f in this problem? What is the value of the integral, namely this one?
\int_{-\pi/4}^{\pi/4} 3 cos(x)dx

a is -pi/4

b is pi/4

f is 3cosx

integral is 0. cause odd function right?

 

[micromass]

Yes, except that the function snt odd and the integral doesn't equal 0.

 

[kings13]

Yes, except that the function snt odd and the integral doesn't equal 0.

3cos(pi/4)-3cos(-pi/4)=2.12-2.12. or is it plus? if it is plus then what next? multiply by 1/b-a?

 

[micromass]

Since when does \int{3\cos(x)dx}=3cos(x)?
What is the integral of a cosine?

 

[kings13]

Since when does \int{3\cos(x)dx}=3cos(x)?
What is the integral of a cosine?

not thinking straight. sorry I am doing an essay at the same time but that's really no excuse

3sin(pi/4)-3sin(pi/4)=

2.12132+2.12132


now what?

 

[micromass]

Now you need to calculate

\frac{1}{b-a}\int_a^b{f(x)dx}

thus plug in everything you know, and you will get a certain number. Now you only need to find a c such that f(x)=3cos(c) equals that very number.

 

[kings13]

Now you need to calculate

\frac{1}{b-a}\int_a^b{f(x)dx}

thus plug in everything you know, and you will get a certain number. Now you only need to find a c such that f(x)=3cos(c) equals that very number.

well the integral is 4.24. the 1/b-a is .63662

4.24x.63662=2.7

2.7=3cos(x)? what? how in the world do you solve that

 

[Mark44]

The integral is actually 3√2 and the length of the interval is actually ∏/2. You'll get better results if you leave your intermediate results in their exact forms rather than rounding to a random number of decimal places.

If you have a = b cos(x), there's an inverse trig function that will be helpful.

 

[kings13]

inverse cosine i got it right

thanks for the help

 

[kings13]

The integral is actually 3√2 and the length of the interval is actually ∏/2. You'll get better results if you leave your intermediate results in their exact forms rather than rounding to a random number of decimal places.

If you have a = b cos(x), there's an inverse trig function that will be helpful.

the online thing wanted decimals but yea i shud leave it as that for the test.

before someone calls me dumb for not using inverse trig i solved it before reading the last help