MATH 1680 Lecture Notes - Lecture 1: Riemann Sum, Multiple Integral

(1 point) Sketch the region enclosed by the curves 9 - Decide whether to integrate with respect to r or y. Then find the area of the region. y2 and y-9. Area-

quiz6.1: Problem 6 Previous Problem Problem List Next Problem (1 point) Find the area of the region between the curves y and y 2 -2 Area between curves - Preview My Answers Submit Answers You have attempted this problem 5 times. Your overall recorded score is 0%. You have unlimited attempts remaining. Type here to search n.

уг This area can be computed in two different ways (1 pont) Consider the area between the graphs a, + 2y . 26 and ® + 9 using integrals First of all it can be computed as a sum of two integrals where a li and Aternatively this area can be computed as a single integral blv) dy where o h(g)- Either way we find that the area is tti and Note: You can earn partial creait an this problem

Instructions: You may work with other students, but be sure to write up an individual solution and list everyone you worked with. Note: I ask that you do not explicitly compute the area/volume, just write down the integral. However, I have given answers so you can check your solution if you wish. There are various online resources for computing integrals, which you may use to check your answer. I need to see your work! If I see a paper with just a list of integrals, it will not receive full credit. Set up an integral (or sum of integrals) which gives the area of the region enclosed by the given curves. y = sin(pix/2), y = x2 - 2x (Ans: 4/3 + 4/pi) y = 4x2, y = x2, y = 16. (Ans: 128/3) First do it with respect to y, then do it with respect to x. Which method did you find superior? Set up an integral which gives the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. x = y - y2, x = 0; about the y-axis (Ans: pi/30) y = sin x, y = cos x, 0 x pi/4; about y = - 1 (Ans: ( -3/2)pi) y = x, y = 0, x = 2, x = 4; about x = 1 (Ans: 76 pi/3) Use the method of cylindrical shells to set up an integral which gives the volume of the solid generated by rotating the region bounded by x + y = 3 and x = 4 - (y - 1)2 about the x-axis. (Ans: 27pi/2)