Chapter 07

Page 1

January 27, 2005 11:45

L24-CH07

Sheet number 1 Page number 290

black

CHAPTER 7

Applications of the Definite Integral in Geometry, Science, and Engineering EXERCISE SET 7.1

2

2 (x + 1 − x)dx = (x /3 + x − x /2) = 9/2 2

1. A = −1

4

2. A =

3

2

−1

4 √ ( x + x/4)dx = (2x3/2 /3 + x2 /8) = 22/3

0

0 2

3. A =

2 (y − 1/y 2 )dy = (y 2 /2 + 1/y) = 1

1

4. A =

1 2

2 (2 − y 2 + y)dy = (2y − y 3 /3 + y 2 /2) = 10/3

0

0

4

(4x − x2 )dx = 32/3

5. (a) A =

16

(b) A =

0

√ ( y − y/4)dy = 32/3

0

y (4, 16) y = 4x y = x2 5 x 1

6. Eliminate x to get y 2 = 4(y + 4)/2, y 2 − 2y − 8 = 0, (y − 4)(y + 2) = 0; y = −2, 4 with corresponding values of x = 1, 4.

1

(a) A =

√ √ [2 x − (−2 x)]dx +

0

1

=

4 xdx + 0

4

√ [2 x − (2x − 4)]dx

4

√ (2 x − 2x + 4)dx = 8/3 + 19/3 = 9

4

−2

(4, 4)

y2 = 4x

y = 2x – 4 x

1

1

(b) A =

y

[(y/2 + 2) − y 2 /4]dy = 9

290

(1, –2)


Turn static files into dynamic content formats.

Create a flipbook
Issuu converts static files into: digital portfolios, online yearbooks, online catalogs, digital photo albums and more. Sign up and create your flipbook.
Chapter 07 by Faheem Ajmal - Issuu