Find the area of one side of the "winding wall" standing orthogonally on the curve y= x^2 , 3<= x <=5 and beneath the curve on the surface f(x, y) = x + √y.

The required area is 131.6626

Step-by-step explanation:

Given that;

equation of the curve;  y=x², 3≤ x ≤5

and equation of the surface; f(x,y) = x + √y

Find the Area A = ∫_c ( x + √y) dS

Find the parametrization of the curve.

so let x = a then y = a²

then dx/da = 1, dy/da = 2a

since 3≤ x ≤5 and x = a hence; 3≤ a ≤5

so the area of one side of winding wall will be;

A = ∫_c ( x + √y) dS

= ⁵∫₃ ( a + √a²) √[(dx/da)² + (dy/da)²] da

= ⁵∫₃ ( a + a ) √[(1)² + (2a)²] da

= ⁵∫₃2a√(1 + 4a²) da

= [1/6(4a² + 1 )^3/2)]₃⁵

= - 37/6×√37 + 100/6×√101

= -37.5103 + 169.1729

= 131.6626

Therefore the required area is 131.6626

to plot points   for x just start at the origin (middle) and go to the left however many times it say(if the number is a positive) if the number is a negative then go right however many times it says if it is 0 go nowhere

now keep you pencil there and go up however many times it says on y(if it is positive) if it is negative then go down however many times it says. if it says 0 go nowhere.

you have just plotted a point! now when you finish plotting all of them connect them with a ruler

plot each point as (-3, 7), (0,4), (3,1), (8,-4)   in the parenthesis on the left of the comma is x and the right is y.

connie < felicia < stew

step-by-step explanation:

stew:

we need to find the slope

m = (y2-y1)/ (x2-x1)

    = (2650-795)/(10-3)

    = 1855/7

265 words per minute

connie:

we need to find the slope

m = (y2-y1)/ (x2-x1)

we have two points (0,0) and (4,800)

m = (800-0)/(4-0)

  m = 800/4

    200 words per minute

felicia:

260 words per minute

200< 260 < 265

connie < felicia < stew