The Mean Value Theorem for Integrals states that for a continuous and positive function f on a closed interval [a,b], there must exist a number c in [a,b], such that:

Find all values of c in the interval [0,90], which satisfies the Mean Value Theorem for Integrals for the function R(t) given in Question 9. Show the equation needed to be solved to find the value of c. (Note: You may find c using any method you choose. That is, you can solve the equation graphically and/or with a CAS.)

Question

The Mean Value Theorem for Integrals states that for a continuous and positive function f on a closed interval [a,b], there must exist a number c in [a,b], such that:
 

Find all values of c in the interval [0,90], which satisfies the Mean Value Theorem for Integrals for the function R(t) given in Question 9. Show the equation needed to be solved to find the value of c. (Note: You may find c using any method you choose. That is, you can solve the equation graphically and/or with a CAS.)

kkutie7 · Answer

$$f(c)=\frac{ 1 }{ b-a }\int\limits_{a}^{b}f(x)dx$$

zepdrix · Answer

Where is R(t) from question 9? >.<

kkutie7 · Answer

@zepdrix  R(t) = .4t − 20 cos(π t / 45) + 40

anonymous · Answer

i like the "any method" part http://www.wolframalpha.com/input/?i=1%2F90+times+int+0+to+90+%28.4t+%E2%88%92+20+cos%28%CF%80+t+%2F+45%29+%2B+40%29dt

kkutie7 · Answer

Is that really it? that seems so much more simple than what's going on in my head.

anonymous · Answer

since apparently the answer is $58$ our job it to solve 
$$.4t − 20 cos(π t / 45) + 40 =58$$

kkutie7 · Answer

t here would be c for f(c) though.... right?

anonymous · Answer

solve for $t$
use wolfram

kkutie7 · Answer

alright I'll try that.

anonymous · Answer

http://www.wolframalpha.com/input/?i=.4t+%E2%88%92+20+cos%28%CF%80+t+%2F+45%29+%2B+40+%3D58

anonymous · Answer

Sattty liiiite why u do dis to me my love