Use the rectangles in each graph to approximate the area of the region bounded by y = 5/x, y = 0, x = 1, and x = 5. (Round your answers to three decimal places.)

Question

Use the rectangles in each graph to approximate the area of the region bounded by y = 5/x, y = 0, x = 1, and x = 5. (Round your answers to three decimal places.)

Answer 1

xy = 5

y = 5/x = 5x^-1

intergral of 5x^-1 = 5lnx

evaluated from 1 to 5

= 5ln5 - 5ln1

= 5ln5 -5(0)

= 5ln5

= about 8.05

y=5/x to the right of y=0, is the top right branch in quadrant I, of a rectangular hyperbola for y=5/x

make two rectangles, with base 2 each, height = y=5/x

left rectangle has height y=5/2 = 2,5, right rectangle has height y=5/4 = 1.25

(2)(2.5+1.25) =2(3.75 = 7.5

7.5 is close to 8.05

use more rectangles and it will be closer