<span>Let r(x,y) = (x, y, 9 - x^2 - y^2)
So, dr/dx x dr/dy = (2x, 2y, 1)
So, integral(S) F * dS
= integral(x in [0,1], y in [0,1]) (xy, y(9 - x^2 - y^2), x(9 - x^2 - y^2)) * (2x, 2y, 1) dy dx
= integral(x in [0,1], y in [0,1]) (2x^2y + 18y^2 - 2x^2y^2 - 2y^4 + 9x - x^3 - xy^2) dy dx
= integral(x in [0,1]) (x^2 + 6 - 2x^2/3 - 2/5 + 9x - x^3 - x/3) dx
= integral(x in [0,1]) (28/5 + x^2/3 + 26x/3 - x^3) dx
= 28/5 + 40/9 - 1/4
= 1763/180 </span>
Answer:
A. 72 square units.
Step-by-step explanation: I got it right on edginuity.
Answer: first one is : the base salary of an employee and a 9% salary increase; second one is : the price of a winter coat and a 90% discount ; third one is : the number of students attending school last year and a 90% increase from last year ; fourth one is : the cost of groceries and a 9% discount with coupons
Step-by-step explanation:
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Answer:
-(1/3)x+1>y
2x-3≥y
If x<12/7 then 2x-3≥y
and if x≥12/7 then -(1/3)x+1>y