Only do the question (e) with Matlab, please show the code with clear explanations! Thanks in advance!

This question involves double integration of a function f(x,y) over a region R. For each part of this question include a sketch of the region of integration R. (a) f(x,y)=x4y+2xy4 R={(x,y):0yx,1x1} (i) Write down double definite integrals of f(x,y) over R in both ways (integrating with respect to x first, and integrating with respect to y first). (ii) Evaluate either of the above integrals to verify that it is equal to 71. (b) f(x,y)=(x+y) R is the region bounded by the triangle with vertices (0,0),(1,1), and (2,0). Choose an order of integration (either dxdy or dydx ), and evaluate the integral. (c) f(x,y)=xy R={(x,y):x0,y0}{(x,y):x2+y21} Choose an order of integration (either dxdy or dydx ), and evaluate the integral. (d) Swap the order of integration for each the following double integrals. (i) 00xf(x,y)dydx (ii) 00x2f(x,y)dydx (iii) 03x2+13x+1f(x,y)dydx (e) Create MATLAB anonymous functions (function handles) for the integrand f(x,y) and evaluate the integrals from parts (a), (b) and (c) over corresponding regions R