First we will evaluate: ( substitution: u = x² - y², du = - 2 y dy )

=

( than plug in x and 0 )
=

=
= 1/3 x³ ( then another integration )

= 1/3 * 1/4 =
1/12
The correct answer would be C
Answer:
D. The work shown above is correct, and
may not be simplified further.
Step-by-step explanation:
If you add all the exponents of y in first line then we get
4+4+4+4+4+3=23
Which is same as the exponent in original problem.
So first line is good.
Since it is 4th root so each
will turn into y when it moves out of the radical so final answer is correct.
Hence correct choice is "D. The work shown above is correct, and
may not be simplified further." is the correct answer.
2x^2 - 7
we can plug any values of x into this The domain is All Real x.
The graph will be a parabola opening upwards with a minimum value when x = 0 and f(x) will be = -7
so the range is f(x) <= -7 or (-∞, -7]