MATH 1210 Week 9 Assignment

MATH 1210 Week 9 Assignment | Tulane University

Solve the problems below and write up a solution to each problem using complete English sentences and well-organized calculations as appropriate. Your solution will be graded based on mathematical accuracy and clarity of presentation.

Late submissions will not be accepted. You must submit your responses as a single .pdf file that includes all pages of your solution. You may resubmit until the deadline but only the most recent submission will be graded. Quiz submissions will not be accepted via e-mail. After submitting you must download your file to ensure that it submitted properly. See technical instructions on Module Quiz submissions.

Problem 1:

Consider the shaded area below the graph of the function y=x2+1y=x2+1, above the xx-axis and between the lines x=−1x=−1 and x=1x=1, illustrated below.

a.       Use n=4n=4 rectangles and left endpoints for each rectangle to estimate the shaded area. Notice that you cannot be certain whether this estimate is an overestimate or an underestimate because some rectangles miss shaded area and other rectangles include unshaded area.

b.      Use n=4n=4 rectangles and choose your sampled point to guarantee that you get an overestimate of the shaded area.

c.       Use n=5n=5 rectangles and choose your sampled points to guarantee that you get an underestimate of the shaded area.

Problem 2:

Use the Fundamental Theorem of Calculus to evaluate the following definite integrals.

a.     ∫31(x+1)2xdx∫13(x+1)2xdx

b.     ∫1695x3−−√dx∫9165x3dx

c.      ∫π03ex−2sinxdx