Recent content by lap

Thank you very much for all the reply. So, f(x) became a constant with min value and max value ? And this is nothing to do with the mean value theorem for integrals ?

f(a)(b-a) ≤ ∫ f(x) dx from a to b ≤ f(b)(b-a) But then how to get the result f(c)∫ g(x)dx from a to b ?

Homework Statement Let f and g be continuous fuctions on [a,b]. Moreover g(x) > 0 for all x belongs to [a,b]. Show that there is a number c belongs to [a,b] such that ∫ f(x)g(x)dx from a to b = f(c)*∫ g(x)dx from a to b Homework Equations Can you help me to prove this integral...

The question ask to determine whether y = φ(x) = sqrt ( x - 1 ) is a solution of the differential equation 2yy' = 1.

I proved that f(-x)=(-f(x)) and solved it. Thank you very much !

I know the answer is 0 because the positive area canceled the negative area but I don't know how to prove it

The answer is 0 ?

How to integrate ( (sqrt (x^2 - 9))/x )( exp x^2 )( cos 7x )( sin(x^4 + 5x^2 + 100) ) dx ?

Integrate ( (sqrt (x^2 - 9))/x )( exp x^2 )( cos 7x )( sin(x^4 + 5x^2 + 100) ) dx with upper limit = 3 and lower limit = -3 I have tried to use integration by part and set u = ( (sqrt (x^2 - 9))/x )( exp x^2 ) and dv = ( cos 7x )( sin(x^4 + 5x^2 + 100) ) dx