#1 a = ∫[0,3] (3x-x^2) dx = 9/2
#2 Using either discs or shells,
v = ∫[0,4] π(2-x)^2 dy
= ∫[0,4] π(2-√y)^2 dy = 8π/3
or
v = ∫[0,2] 2π(2-x)y dx
= ∫[0,2] 2π(2-x)x^2 dx = 8π/3
#3 I can't make out the function, but the total distance traveled is the arc length of the path followed:
∫√(1+y'^2) dx
over the appropriate interval.
Depending on the graph, it might be easier just to do a geometric evaluation. But since this is a calculus test, I suppose not.
#4 Again, copy/paste mangling, but the average value of f(x) on [a,b] is
(∫[a,b] f(d) dx)/(b-a)
Since 3^cosx is not directly integrable, I suspect an algebraic shortcut is being used, or a numeric approximation is wanted.
#5 f(x) = 1/3 x^3/2
f' = 1/2 x^1/2
s = ∫[0,5] √(1+x/4) dx = 19/3
#6 If the radius is a chord of the circle, then r = 2y = 2√(4-x^2)
Thus, adding up all those slices, each of area πr^2/4, and taking advantage of symmetry,
v = 2∫[0,2] π(4-x^2) dx = 32π/3
1)What is the area bounded by y = x^2 and y =3x?
A)5
B)9/2
***C)8
D)11.2
E)25
i believe it to be 8 but im not sure.
2)The region R is bounded by the x-axis, x = 2, and y = x^2. Which of these expressions represents the volume of the solid formed by revolving R about the line x = 2?
I believe it to be the Integral from 0 to 4( pi(2- sqr root of y)^2
dy
3)Refer to the graph and information: An ant's position during an 8 second time interval is shown by the graph below. What is the total distance the ant traveled over the time interval 2<=t<=8?
What is the total distance traveled by the ant over the time interval 0 ≤ t ≤ 8?
I don't even know what to do with this one
4)The average value of the function g(x) = 3^cos(x) on the closed interval [ − �€ , 0 ] is:
***A)30.980 My answer. Not sure :(
B)18.068
C)7.953
D)4.347
E)1.325
5) Find the length of the arc defined by f(x)= (1/3x^3/2) on the interval from [0,5].
A)12.903
B)5.641
C)6.333
D)12.958
E)6.586
NOT sure
6)A solid has, as its base, the circular region in the xy-plane bounded by the graph of x^2 + y^2 = 4. Find the volume of the solid if every cross section by a plane perpendicular to the x-axis is a quarter circle with one of its radii in the base.
PLEASE HELP ME with what you can. You dont have to answer all but help me with the easy short ones PLEASE. My test in close date and this is a big thing for me. Thank you :)
1 answer
1 answer