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How do you find the area between #y=x^3# and #y=6-x#?

Answer 1

Evelyn Agard

There is no region bounded by just those two curves. So there is no area. (Or no finite area, if you prefer.)

Here is the graph:

graph{(y-x^3)(y-6+x)=0 [-15.22, 16.82, -4.36, 11.66]}

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Answer 2

Samantha Adkison

To find the area between the curves (y = x^3) and (y = 6 - x), follow these steps:

Find the points of intersection of the curves by setting them equal to each other: (x^3 = 6 - x).
Solve for (x) to find the x-coordinates of the points of intersection.
Integrate the difference of the upper curve (6 - x) and the lower curve (x^3) over the interval where they intersect.
Take the absolute value of the resulting integral to ensure a positive area.

This process will give you the area between the curves (y = x^3) and (y = 6 - x).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.