Russell has been training for the Emerald Valley Race. The first week he trained, he ran 5 days and took the same two routes eac
2 answers:
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Answer:
C and E
Step-by-step explanation:
To solve this problem, let's plug in each coordinates into the equation.
A:
- A. cannot be the answer, as 50 does not equal -7.
B:
- B. cannot be the answer, as 11 does not equal -7.
C:
- C. can be the answer, as -7 does equal -7.
D:
- D. cannot be the answer, as -31 does not equal -7.
E:
- E. can be the answer, as -7 does equal -7.
Answer:
The integral is equal to for an arbitrary constant C.
Step-by-step explanation:
a) If then
so the integral becomes
. (the constant of integration is actually 5C, but this doesn't affect the result when taking derivatives, so we still denote it by C)
b) In this case hence
. We rewrite the integral as
.
c) We use the trigonometric identity is part b). The value of the integral is
. which coincides with part a)
Note that we just replaced 5+C by C. This is because we are asked for an indefinite integral. Each value of C defines a unique antiderivative, but we are not interested in specific values of C as this integral is the family of all antiderivatives. Part a) and b) don't coincide for specific values of C (they would if we were working with a definite integral), but they do represent the same family of functions.