682
Chapter 6 | Applications of Integration
6.4 EXERCISES For the following exercises, find the length of the functions over the given interval. 165. y =5 x from x =0 to x =2
evaluate the integral exactly, use technology to approximate it.
171. y = x 3/2 from (0, 0) to (1, 1) 172. y = x 2/3 from (1, 1) to (8, 4)
166. y = − 1 2
x +25from x =1 to x =4
3/2
173. y = 1 3 ⎛ 174. y = 1 3 ⎛
⎞ ⎠
167. x =4 y from y =−1 to y =1 168. Pick an arbitrary linear function x = g ( y ) over any interval of your choice ( y 1 , y 2 ). Determine the length of the function and then prove the length is correct by using geometry. 169. Find the surface area of the volume generated when the curve y = x revolves around the x -axis from (1, 1) to (4, 2), as seen here.
⎝ x 2 +2
from x =0 to x =1
3/2
⎞ ⎠
⎝ x 2 −2
from x =2 to x =4
175. [T] y = e x on x =0 to x =1 176. y = x 3 3 + 1 4 x from x =1 to x =3 177. y = x 4 4 + 1 8 x 2 from x =1 to x =2 178. y = 2 x 3/2 3 − x 1/2 2 from x =1 to x =4
3/2
179. y = 1 27 ⎛
⎝ 9 x 2 +6 ⎞ ⎠
from x =0 to x =2
180. [T] y = sin x on x =0 to x = π For the following exercises, find the lengths of the functions of y over the given interval. If you cannot evaluate the integral exactly, use technology to approximate it. 181. y = 5−3 x 4 from y =0 to y =4 182. x = 1 2 ⎛ ⎝ e y + e − y ⎞ ⎠ from y =−1 to y =1
170. Find the surface area of the volume generated when thecurve y = x 2 revolves around the y -axis from (1, 1) to (3, 9).
183. x =5 y 3/2 from y =0 to y =1 184. [T] x = y 2 from y =0 to y =1 185. x = y from y =0 to y =1
3/2
186. x = 2 3 ⎛
⎞ ⎠
⎝ y 2 +1
from y =1 to y =3
187. [T] x = tan y from y =0 to y = 3 4 188. [T] x =cos 2 y from y = − π 2
For the following exercises, find the lengths of the functions of x over the given interval. If you cannot
to y = π 2
This OpenStax book is available for free at http://cnx.org/content/col11964/1.12
Made with FlippingBook - professional solution for displaying marketing and sales documents online