Sketch the region enclosed by 2y=3sqrt(x), y=4, and 2y+4x=7. Decide whether to integrate with respect to x or y, and then find t

Question

2 years ago

14

he area of the region.

1 answer:

iragen [17] · Answer 1 · 2023-05-14T08:23:00+03:00

The area of the region is 183/100 Square units

<h3>Calculations and Parameters</h3>

y = (5/2) sqrt(x) = 4

===> 25x = 64

===> x = 64/25

y = (5/2)sqrt(x) = (-3x+8)/2

===> 25x = 9x^2 - 48x + 64

===> x = 1

Area = Integral ( 0 to 1) ( 4-(-(3/2)x -4))dx + Int(1 to 64/25)(4 - 2′5 sqrt(x)dx

= (3x^2/4) ( from 0 to 1) + (4x - (5/3)x^(3/2)) from 1 to 64/25) = 3/4 + 27/25

Area = 183/100

Hence, we can see that the area of the region is 183/100 Square units