Please help!

I(r ) = ex dx. (a) Estimate the value I(1) using 4 rectangles with same base length and midpoints as the choice of sample points. hs (b) Find the critical points and inflection points for the function y = e-x2 . Use this information to sketch the graph of y = e- and, in your picture, indicate what lim I(r) T -+ 00 represents. (c) Use one of our RIEMANN.m scripts (left, right or midpoint) to estimate I(r) using 10r rectangles when: (i) r = 1; (ii) r = 5; (iii) r = 10; (iv) r = 100. Use those estimates to obtain an estimate for lim I(r). Now, square this value. What 1 -+00 mathematical constant does this squared value seem to be an approximation of