Sketch the region r defined by 1≤ x≤ 2 and 0≤ y≤ 1/x^3
a) find (exactly the number a such that the line x = a divides r into two parts of equal area.
b) then find (to 3 places) the number b such that the line y = b divides r into two parts of equal area.

On the attachment, there is the graph for the region "R" and the calculations for the value a and b. 

the theory is that you have to choose a value that is between the range and assume that this value will divide the area into two equal parts. This is done for x = a

For
"y" you have to change the integral from dx to dy and you have to divide the region into 2 parts, given that the area cannot be calculated by 1 integral equation, so you proceed to calculate the rectangular area and take this area into consideration, for the same procedure as before. 

Then you calculate again the value y = b and that's it.