quiz2sol - Math 241 CD3/CD4 Quiz 2 1. (5 points) Evaluate 2...

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Unformatted text preview: Math 241 CD3/CD4 Quiz 2 1. (5 points) Evaluate 2 0 4 y2 Name: y cos(x2 )dxdy . √ 0 4 √ y= x 2 1.5 1 0.5 4 x 4 = 0 y cos(x2 )dydx = 0 4 y2 cos(x2 ) 2 = sin 16/4. dx y =0 = 1 2 3 4 0 x 1 cos(x2 )dx = sin(x2 ) 2 4 0 2. Setup but DO NOT evaluate the integrals for the following. (a) (5 points) The area of the region bounded by y = x2 , y = x2 − 5, and y = 4. 4 2 −2 1 2 3 4 2 x2 3 4 dydx + x2 −5 √ y +5 √ − y +5 dydx + −2 x2 −5 √ 4 −y 0 √ − y +5 2 dydx. x2 −5 √ y +5 4 -3 -2 -1 −3 0 -2 or −5 dxdy + dxdy + 0 √ y dxdy. -4 (b) (5 points) The volume of the solid cut out of the sphere x2 + y 2 + cylinder x2 + y 2 = 1. 3 z2 2 = 9 by the 2 1 −1 √ 1−x2 2 √ 9−x2 −y 2 1 -3 -2 -1 1 2 3 -1 or 0 √ √ − 1−x2 −2 9−x2 −y 2 √ 2 9−r 2 1 2π 0 √ −2 9−r 2 dzdydx rdzdrdθ. -2 -3 3. (5 points) Evaluate x2 + y 2 ≤ 3. 1.75 1.5 1.25 1 0.75 0.5 0.25 -1.5 -1 -0.5 0.5 1 1.5 R x2 + y 2 + 1dA, where R is the upper half part of the disk π √ 0 3 x2 R + y2 + 1dA = 0 π √ r2 + 1rdrdθ √ r= 3 π = 0 12 (r + 1)3/2 3 dθ = r =0 0 7 7π dθ = . 3 3 1 ...
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