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Question
Which of the following is the best integration technique to use for ∫2x(x2 + 1)5 dx?
A) The product rule.
B) The chain rule.
C) The power rule.
D) The substitution rule
What is the value of R(g) = f(g)/h(g), f (-4) = 2, h(-4) = 0, f '(-4) = 6, h'(-4) = 3.
A) 0
B) ½
C) 2
D) This is indeterminate.
1) As I look at what we are integrating, the first thing that pops into my head is to let u = x² + 1, du = 2x dx, which is the chain rule. However, actual integration is done on ∫u^5 du,
so the integration, in my opinion, is done with the power rule.
The chain rule is used to put it in the form where it can be integrated, but that is not the actual integration.
2) For R(g) = f(g)/h(g), they give us all the values we need to determine the value when g is -4. However, no where does the problem state that g = -4, so I would say the answer were (D).
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