Consider the solid that lies above the rectangle (in the xy-plane) R = [-2, 2] X [0, 2] and below the surface z = x2 - 6y + 12.
A) Estimate the volume by dividing R into 4 rectangles of equal size, each twice as wide as high, and choosing the sample points to result in the largest possible Riemann sum.
B) Estimate the volume by dividing R into 4 rectangles of equal size, each twice as wide as high, and choosing the sample points to result in the smallest possible Riemann sum.
C) Using iterated integrals, compute the exact value of the volume.

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step-by-step explanation:

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.

i don't see any

step-by-step explanation: