Describe in plain english what the radius of gyration is

Question

1: Knowledge.

A. u-substitution in integrals is the integral form of what Calc 1 property?

B. Describe in plain English what the radius of gyration is.

C. State the definition of an improper integral _a∫^∞ f (x)dx. Let F'(x) = f (x).

D. In R³ (3-space), what does z usually represent?

E. Finding partial fractions is the inverse of what process?

F. Integration by parts is the integral form of what Calc 1 property?

G. What is an antiderivative of a function? (Hint: Do not use the word "opposite" in your answer").

H. Explain what lets you know you can use u-substitution to evaluate an integral.

I. Explain what lets you know you should use integration by parts to help evaluate an integral.

J. Explain what lets you know you should use partial fractions to help evaluate an integral.

k. Consider the following Integral, ∫ e^x sin(x) dx. This function is able to be evaluated with integration by parts by applying integration by parts twice. Explain how this is possible even though neither function will "diminish".

Section 2: True or False.

1, Let F(x) be an antiderivative of a function f (x). Then consider the following statements:

i. F(x) is unique.

ii. F(x) is a polynomial.

iii. There are infinitely many anti derivatives.

Choose the best choice and explain why:

A. Both (i) and (ii) are true.

Both (ii) and (iii) are true.

C. Only (i) is true.

D. Only (iii) is true.

E. None of the statements are true.