<h3>
Answer: x*a^2 or a^2*x</h3>
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Work Shown:
a^(b+2) = a^b*a^2 ... break up the exponent
a^(b+2) = x*a^2 ... replace a^b with x
We don't know the value of 'a' nor the value of x, so we cannot evaluate further. This is the same as a^2*x because order of multiplication does not matter. For example, 2*3 = 6 and 3*2 = 6, so 2*3 = 3*2.
R is (-3,8)
to get from p’ to q’, you subtract 7 from the x’ value, and add 5 to the y’ value. so you do the same to get from q’ to r’
Interesting that only integrals along the
-axis are suggested when integrating along the
-axis would be much simpler... Anyway, you have to split the interval of integration into two. The "height" of the region is not uniform over the entire interval.
When
, we have
. When
, we have
. Then the area we want is given by

which seems to agree with the last option.