Tutorial_7 - (a Z 8 Z 2 3 √ y e x 4 dxdy(b Z 2 √ ln3 Z...

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NATIONAL UNIVERSITY OF SINGAPORE Department of Mathematics MA 1505 Mathematics I Tutorial 7 1. Calculate the following iterated integrals: (a) Z b 0 Z a 0 ( x 2 + y 2 ) dxdy (b) Z 2 1 Z 1 0 xy 4 - x 2 dxdy . Ans : (a) 1 3 ab ( a 2 + b 2 ) (b) 3 - 3 3 / 2 2. Evaluate the following double integrals: (a) ZZ R e x 2 dA , R is the region bounded by y = 0 , y = x, x = 1. (b) ZZ R ( x + y ) dA , R is the region bounded by the two curves y = x, y = x 2 . Ans : (a) 1 2 ( e - 1) (b) 3 10 3. Evaluate the double integral RR R x dA where R is the region as shown below. Ans : 25 4. Evaluate the integral Z 1 0 Z 1 - x 2 0 e x 2 + y 2 dydx by converting it to polar coordinates. Ans : 1 4 π ( e - 1) 5. Evaluate the following integrals by reversing the order of integration.
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Unformatted text preview: (a) Z 8 Z 2 3 √ y e x 4 dxdy (b) Z 2 √ ln3 Z √ ln3 y/ 2 e x 2 dxdy Ans : (a) 1 4 ( e 16-1) (b) 2 6. Find the volume of the solid whose base is the region in the xy-plane that is bounded by the parabola y = 4-x 2 and the line y = 3 x , while the top of the solid is bounded by the plane x-z + 4 = 0. Ans : 625/12 MA1505 Tutorial 7 7. Find the volume of the solid bounded by the cylinders x 2 + y 2 = r 2 and y 2 + z 2 = r 2 . Ans : 16 3 r 3 2...
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Tutorial_7 - (a Z 8 Z 2 3 √ y e x 4 dxdy(b Z 2 √ ln3 Z...

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