question archive Let R be the region bounded by y = 2 _ x y -2+ x and x = 1
Let R be the region bounded by y = 2 _ x y -2+ x and x = 1
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Let R be the region bounded by y = 2 _ x y -2+ x and x = 1. A. Sketch/graph R. B. Set up the integral(s) that give the area of R with respect to x. Your bounds must be in exact form. C. Set up the integral(s) that give the area of R with respect to y. Your bounds must be in exact form. D. Find the area of R using your answer to either B or C. You may use the table of integrals for this problem, though you do not need to. Hint: one of these integrals is significantly easier than the other, though it may require some simplification. The other is still doable with a little bit of u-substitution.
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Solution:- 1 2 - in 2 + 52 and M = 1 A ky = z - in n=(4-2) 12 (I , 1 ) 1 = 1 R ( 1 1 0 . 3 33 ) 08 ( 1 1 3 ) J = 1 The area of R with sespect ton is A = 2 - 57 2 + 522/ dn O The area of R with respect to y is A 2, dy WH A = 1 ( 1 - 42 - 4 + ? ) dy The, A = 0.3944 sq. unit sense, Area of region R = 0. 3944 sq. unit
Quick Theory ( 1 ) Area with sesped to n JL = f (on ) 72 = g (2 ) m= a X = b b A = 1 ( 41 - yz ) do a ( 1! ) Area with respect to y y =d n s = fly) n 2 = gly ) y = c in 2 A = ( M 1 - 2/2) gly C
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