Question

Find the maximum value for...

a)The integral from a to b of (6+x-x^2)dx

b) f(x)=ln(x)-e^x

c) The Jacobi Theta Function

d) The Integral of ln(ln(1/x))dx

Answer 1

So the general technique necessary is to differentiate to find minimas and maximas of functions.

Answer 2

For example for part a, let's say the integral evaluates to F(b)-F(a). Then, you want to find the a which gives the smallest value of F(a) and the largest value of b which gives the largest value of F(b). (Also note that a<b). You can find the largest value of F(b) by using differentiation to find the maxima. Then for this particular Q, if you let a tend to negative infinity...