What is the coefficient of the first time in 6x^7-5x^3+9x^2-1
1 answer:
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Answer:
First number: 15
Second number: 21
Third number: 84
Step-by-step explanation:
To approximate the volume with 8 boxes, we have to split up the interval of integration for each variable into 2 subintervals, [0, 1] and [1, 2]. Each box will have midpoint that is one of all the possible 3-tuples with coordinates either 1/2 or 3/2. That is, we're sampling
at the 8 points,
(1/2, 1/2, 1/2)
(1/2, 1/2, 3/2)
(1/2, 3/2, 1/2)
(3/2, 1/2, 1/2)
(1/2, 3/2, 3/2)
(3/2, 1/2, 3/2)
(3/2, 3/2, 1/2)
(3/2, 3/2, 3/2)
which are captured by the sequence
with each of being either 1 or 2.
Then the integral of over
is approximated by the Riemann sum,
(compare to the actual value of about 4.159)