integral question

Question

If ∫ ⁵₂  f(x) dx=4 and ∫⁷₂ f(x)=-3 then ∫⁵₇ f(x)dx=

 

I got 7 and then redid it and got 12. am I missing something? Whats the right answer?

Answer 1

Not sure how you got 12. 

 

Take a look at this:

 

∫7₂  =  ∫⁵_{2 +} ∫⁷₅

 

 

 

 

Answer 2

                                            _b

Let f(x) = dg(x)/dx.  Hence ∫ f(x) dx = g(b)-g(a):

                                           ^a

 

 

     g(7) - g(2) = g(7) - g(5) + g(5) - g(2)

 

     g(7) - g(2) - (g(5) - g(2)) = g(7) - g(5)

 

     -3 - 4 = g(7) - g(5)

 

    -7 = g(7) - g(5)