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

This preview shows pages 1–2. Sign up to view the full content.

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.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

{[ snackBarMessage ]}

### Page1 / 2

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online