Question

f(x)=x^3 and g(x)= 2x-x^3, the area enclosed between the origin and the intersection with a positive x is?

Answer 1

do you know how to do a double integral or just single integrals there are several ways to tackle this, in either case find the intersection point first of all.

Answer 2

tell me what it is and i will help you finish the problem, also make a quick sketch of the area first

Answer 3

intersection point is x=1

Answer 4

alright so that will become your upper bound of integration.

Answer 5

So 1 is your outer boundary, the origin the other: (0,1)

Answer 6

it asks for the area between the origin and the intersection, so you mean the area between the 2 curves?

Answer 7

yup

Answer 8

alright so on your sketch which function lies higher in the y direction?

Answer 9

g(x)

Answer 10

correct so the area between 0,0 and g(x) - the area between 0,0 and f(x) will be the area that is squeezed in between

Answer 11

soo..\[\int\limits_{0}^{1}g(x)dx-\int\limits_{0}^{1}f(x)dx\]

Answer 12

you can also do a double integral but im not sure what level of calculus you are studying so this should do in any case

Answer 13

so in any case, the function that lies higher will subtract the lower function? to find the area between the curves

Answer 14

yep, because if you think of it visually g(x) lies higher in the y direction so the area under g(x) is bigger than f(x), Then subtracting the area under f(x) from g(x) will give you the are between g and f

Answer 15

thank you so much! :)

Answer 16

np

Answer 17

Be careful slim, to your question, that is the case in this problem because you are integrating along the x axis. Be alert that in the future you tackle some problem along the y axis and it would be certainly different. But don't worry about that until you get to it.

Answer 18

alright, i'll keep that in mind, thank you! :)