4. Figure below shows an example three layered-formation. Note that the notation is slightly changed 'om the one used in class: the stresses in layers are denoted S.- (i=1,2,3), and the total fracture (crack) length is 2a. The length of the pay zone is h=b2+b3 (note that in general case, center of the crack is not necessarily aligned with the center of the pay zone). We denote the net pressure Pnefy) =Pf - S(y) along the length of the fracture to be difference between the uid pressure in the fracture Pf (assumed uniform over length of the fracture) and S(y) is stress S,- in the appropriate layer at the position y. a) For this geometry, the stress-intensity factor at the top of the acnue can be determined by calculating the following integral _ 1 \" N/a + y Kltap m _a Pnet(y) aydy Find KIM, as a function of a, b 2, b 3, Pac and in situ stresses S,-. This is a calculus exercise. (Note that one could similarly dene Ktbmm)