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MAT 1322M1 2003 - MAT 1322 MIDTERM 1 VERSION A 1[2 points...

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Unformatted text preview: MAT 1322 MIDTERM 1, VERSION A 1. [2 points, 5.10 #19] Determine if the integral R ∞ 2 1 x (ln x ) 2 dx is convergent or divergent and evaluate if it is convergent. A.1 B.2 . 51 C.0 . 50 D.5 . 33 E.1 . 44 F.divergent Solution . R ∞ 2 1 x (ln x ) 2 dx = R ∞ ln 2 1 u 2 du [ u = ln x ] =- 1 u ∞ ln 2 = 0 + 1 ln 2 . = 1 . 44 2. [2 points, 6.1 #11] Find the area of the region enclosed by the curves y 2 = 2 x and 2 x- 2 y = 3. A.5 . 33 B.4.77 C.3 . 55 D.6 E.9 . 01 F.2 . 22 Solution . Intersection y 2 = 2 x and 2 x- 2 y = 3 ⇒ y 2- 2 y- 3 = 0 ⇒ ( y- 3)( y + 1) = 0 ⇒ y =- 1 , 3. A = R 3- 1 [( 1 2 (2 y + 3)- 1 2 y 2 ] dy = 1 2 R 3- 1 (2 y + 3- y 2 ) dy = 1 2 y 2 + 3 y- 1 3 y 3 3- 1 = 1 2 32 3 = 5 . 33 3. [2 points, 6.2 #13] The region enclosed by the curves y = 3 √ x, x = 1 , y = 0 is rotated about the line x = 2. Find the volume of the resulting solid. A.11 . 44 B.7.17 C.5 . 10 D.12.57 E.10 . 11 F.6 . 73 Solution . y = 3 √ x ⇒ x = y 3 A = R 1 π [( y 3- 2) 2- 1 2 ] dy = 15 7 π . = 6 . 73 4. [2 points, 6.2 #31] The base of a solid is the region { ( x, y ) | x 2 ≤ y ≤ 2 } . Cross-sections perpendicular to the y-axis are semicircles. Find the volume of the solid....
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MAT 1322M1 2003 - MAT 1322 MIDTERM 1 VERSION A 1[2 points...

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