Reverse the following integrals dzdy dxdy dxdy 2 + 1-2 2 dydx +! dydx J-11-V1+2
1. Evaluate the following integrals: (1) SH/2 V1 + cos x 1 J-1/4 1+sin x 2 Cind the ravimatolsraren of the regionbounded by the Uron
Calculate the following double integrals. Be sure to include a sketch of the region R. 1. . (2x + 3y)dxdy given R={(x,y)|0 SX < 2,1 sy s3} 2. SR (2xy)dydx given R={(x,y)|0 SX S1,x Sy s 1}
sin y 11. Evaluate the integrals Sysin xy dxdy and sketch the corresponding 0 0 region. (10pc
Let the region R be the triangle with vertices (1, 1), (1,3), (2, 2). Write the iterated integrals for SSR f(x, y)dA 1. in the “dydx” order of integration 2. in the “dxdy” order of integration
Exercise 6. Double integral in rectangular coordinates (10 pts+10 pts) Let I secx dydx. 2) By reversing the order of integration of I, we get: a. I = $ S secx dxdy b. 1= SS secx dxdy c. IESU secx dxdy d. 1 = secx dxdy
1. Evaluate triple integrals. sinx sin y dzdydx (a)Jo So (b) o JoV dz dxdy
Question 13 Consider the iftegral 22 -dz V1 + 23 Which of the following integrals is equivalent to this under the substitution u = 1 + 23? u2 du V1+23 Ta s rudu (x - 1) du Set 3 du yu 1 du yu
What are S, L, and J for the following states? (Enter half integrals as n/2, for example 1/2.) S L J Iso 0 0 0 129112 | 401/2 2H11/2|
Q2 Question 2 1 Point If Q is a rectangle and f:Q → Ris nonzero only on a closed subset of measure zero, then So f = 0. true false Save Answer Q3 Question 3 1 Point Let f : [0,1] × [0, 1] → R be a bounded function such that the integrals So So f(x)dydx and So So f(x)dxdy both exist and are equal. Then S10,1)*(0,11 f exists. true false Save Answer
Problem #11: Let v1 = (-1,2,-1) and v2 = (-2,-1,-2). Which of the following vectors are in span{V1, V2}? (i) (-3,1,-2) (ii) (-5,0,-4) (iii) (-8, 1,-7) (A) none of them (B) (i) and (ii) only (C) (i) only (D) (iii) only (E) (ii) only (F) all of them (G) (i) and (iii) only (H) (ii) and (iii) only Problem #11: Select Just Save Submit Problem #11 for Grading Attempt #1 Attempt #2 Attempt #3 Problem #11 Your Answer: Your Mark: