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Review Questions in Calculus

The integrals wouldnt paste from word so I had to write them in

If an improper integral is found to have a finite solution, then:
A) The solution will always be some multiple of π.
B) You've done something wrong.
C) The function being integrated converges.
D) The function being integrated diverges.
If f(x) = x^2, find its solid volume for x∈[-3, -1].

A) 763.41 units3
B) 81.68 units3
C) -763.41 units3
81.68 units2

If Mx > My for planer figure Z, then what can we say about Z, if anything?

A) That there is an imbalance along the x-axis.
B) It's easier to rotate around the y-axis than the x-axis.
C) It's easier to rotate around the x-axis than the y-axis.
D) That you made an error in calculations since Mx ≠ My.
The centroid of a planer figure is the same as its:
A) moment.
B) balance point.
C) boundary condition.
D) constant of integration.
The development of the arc length algorithm was a lot like that used to:
A) calculate areas under a curve.
B) differentiate area.
C) determine the slope of a curve.
D) Newton's Method.
The first steps to solving Integral 5/(2x+1)(x-2) dx is to find the constants, A and B, in:

A) 5 = A(2x + 1) + B(x - 2)
B) 5/(2x+1)(x-2)= A/(x-2)+B/(2x+1)
C) 5/(2x+1)(x-2)= AB/(2x+1)(x-2)
D) 5/(2x+1)(x-2)=A/(2x+1)(x-2) + B/(2x+1)(x-2)

Integral 1/(x^2+2x+1)+1 dx=

A) cot(x+1) + C
B) tan-1(x2+2x+1)
C) cot(x2+2x+1) + C
D) tan-1(x+1) + C
What is the arc length of h(x) = x^0.5 for x∈[0, 5]?

A) ≈0.158 units
B) 19/3 units
C) ≈2.2 units
D) There is no method to determine this.

Which of the following is in the correct general form to find solid volume revolved around an axis with a central hollow core?
A) integral [f(q)]^2 dq
B) integral pi[f(q)]^2 dq
C) integral [f(q)]^2-[g(q)]^2 dw
D) integral pi[[f(q)]^2-[g(q)]^2] dq

Which of the following is the method by which to calculate y with a line above it?



Which of the following is an appropriate selection for u and dv if solving this expression by the process of integrating by parts: ∫ln(x) dx?
A) u = ln(x), dv = dx
B) u = 1, dv = ln(x) dx
C) u = x, dv = ln(u) dx
D) There is insufficient information to solve this problem.

Which of the following is a technique used to solve integration problems of greater complexity?
A) Trigonometric substitution.
B) Using previously developed solutions.
C) Integration by parts.
D) All of the above.

Which planer shape lends itself to be the easiest to rotate regardless of the orientation of the axis about which it is to be rotated?
A) A square
B) A trapezoid
C) A circular disk
D) An ellipsoid

Solution Summary

This posting contains the solution to the given problems.