eNCLOSED BY Y=X^3 AND Y=X^4 HOW DO I FIND A&B

Question

I DONT KNOW HOW TO FACTOR X^3-X^4

Answer 1

Are you looking for the area enclosed by y = x³ and y = x⁴? 

To find the intercepts of the two curves, and thus the boundaries for the area enclosed, you need to find where the equations are equal (which you've done).

from x³ - x⁴ = 0 we can take out the common factor of x³ to get:

x³(1-x) = 0 (you can check this is correct by distributing the x³)

From here we can see that x = 0 and x = 1 will satisfy the equation, so those are our boundaries for the integral. Since y = x³ is greater than y = x⁴ between x = 0 and 1 (you can check this from a graph, even if you google this: y = x^3 and y = x^4), set up the integral to find the area enclosed like so:

Area = ∫₀¹ x³ dx - ∫₀¹ x⁴ dx

which integrates to: Area = [x⁴/4]₀¹ - [x⁵/5]₀¹

Which you can now solve by substituting in the values for x. If you need help on this last step, let me know.