Review section 11.3 number 4.

Professor Taylor,

Number 4  in 11.3 there is a substitution made to go from term t to term x giving the answer as cos(x^8) please help and explain this substitution.

Thanks 

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OK, the function f(x,y) is defined as the integral from x to y, of a function of one variable. The f_x that you are supposed to compute is the derivative of the integral with respect to the upper limit of integration.  NOW, something that many people wish they didn't have to remember but always *do* have to remember is the fundamental theorem of calculus, which describes the way that integration is the opposite of differentiation.  What the fundamental theorem gives you is the differentiation with respect to the upper limit gives you the integrand evaluated at the upper limit.   In your case this means that you just get cos(x^8).