What is the answer to the problem above in the picture
1 answer:
Answer: Third option.
Step-by-step explanation:
Some transformations for a function f(x) are shown below:
If , the function is translated "k" units up
If , the function is translated "k" units down.
If , the function is translated "k" units left.
If , the function is translated "k" units right.
In this case you have the following function:
And you know that the function g(x) is obtained by translating the function f(x) 5 units down and 3 units left; therefore, you can conclude that g(x) is:
Finally, simplifying, you get that this is:
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The integrand is continuous everywhere except
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Now, to compute the volume. Via the disk method, we have a volume given by the integral
By the same substitution as before, we can write this as
The half-angle identity for sine allows us to rewrite as
and replacing
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, we have
Like the previous, this require a special function in order to express it in a closed form. You would find that its value is
where
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The integrand is continuous everywhere except
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By the same substitution as before, we can write this as
The half-angle identity for sine allows us to rewrite as
and replacing
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