1. Suppose that D is the region in the xy-plane described by the conditions x >...

 

Transcribed Image Text:

1. Suppose that D is the region in the xy-plane described by the conditions x > 0, ly 1-x, and that the density of D at any point (x, y) is p(x, y) = x. (a) Sketch a picture of the region D. Suppose that we divide [0, 1] up into n equal intervals, each of common width Ax, and with endpoints P {xo, x1,...,xn}. = (b) Let x be some point in [k-1, xk]. If we approximate D by a rectangle on the interval [k-1, k], what is the area of this rectangle in terms of x (i.e., as a formula involving *)? (c) What is the approximate mass of this rectangle? (Still on the interval [xk-1, xk].) (d) Write down a sum approximating the mass ofD. (e) What integral computes the mass of D exactly? (f) What is the mass of D? 1. Suppose that D is the region in the xy-plane described by the conditions x > 0, ly 1-x, and that the density of D at any point (x, y) is p(x, y) = x. (a) Sketch a picture of the region D. Suppose that we divide [0, 1] up into n equal intervals, each of common width Ax, and with endpoints P {xo, x1,...,xn}. = (b) Let x be some point in [k-1, xk]. If we approximate D by a rectangle on the interval [k-1, k], what is the area of this rectangle in terms of x (i.e., as a formula involving *)? (c) What is the approximate mass of this rectangle? (Still on the interval [xk-1, xk].) (d) Write down a sum approximating the mass ofD. (e) What integral computes the mass of D exactly? (f) What is the mass of D?