Question

HELP ME FOR THE BEST TESTIMONY OF YOUR LIFE:

The area of the region bounded by the curves y = f(x) = 2x^3 – 6x^2 – 2x + 6 and y = g(x) = –x^3 + 3x^2 + x – 3 is given by: ?

Answer 1

Refer to the Mathematica attachement which includes a plot.

Answer 2

Sorry, there were some misspellings in the attachment.

Answer 3

What is your answer?

Answer 4

Is this correct?

Answer 5

\[\left\{\int\limits_{-1}^1 \left(3 x^3-9 x^2-3 x+9\right) \, dx,\int\limits_1^3 \left(-3 x^3+9 x^2+3 x-9\right) \, dx\right\}\]Both integrals are equal to 12.
\[\{12,12\}\]

Answer 6

Mathematica likes to leave terms in reverse order.

Answer 7

Can you do this one for me?
Find the area between the curves y = f(x) = x^3 – 3x and y= g(x) = x (the square root of 4-x^2) on the interval 0 ≤ x ≤ 2.

Answer 8

Find the area between the curves y = f(x) = x^3 – 3x and y= g(x) = x (the square root of 4-x^2) on the interval 0 ≤ x ≤ 2.

a)8/3
b)20/3
c)4/3
d)44/3
e)14/3
Which is it? :/

Answer 9

The second solution is attached.
I worked the problem to get answer e)
The curves cross at about x = 1.9 and the area goes negative after that x value.