Answer:
The solution is
Step-by-step explanation:
From the question
The function given is
The indefinite integral is mathematically represented as
Now let
=>
=>
So
Now substituting for u
Please help me quickly! During spring, every three days there is usually 1 rainy day. In a 30 day month, how many days would you
1 answer:
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Answer:
volume V of the solid
Step-by-step explanation:
The situation is depicted in the picture attached
(see picture)
First, we divide the segment [0, 5] on the X-axis into n equal parts of length 5/n each
[0, 5/n], [5/n, 2(5/n)], [2(5/n), 3(5/n)],..., [(n-1)(5/n), 5]
Now, we slice our solid into n slices.
Each slice is a quarter of cylinder 5/n thick and has a radius of
-k(5/n) + 5 for each k = 1,2,..., n (see picture)
So the volume of each slice is
for k=1,2,..., n
We then add up the volumes of all these slices
Notice that the last term of the sum vanishes. After making up the expression a little, we get
But
we also know that
and
so we have, after replacing and simplifying, the sum of the slices equals
Now we take the limit when n tends to infinite (the slices get thinner and thinner)
and the volume V of our solid is
