Question

find the area of the region between y=x^2 and y=x^3 for 0 less than equal to x less than equal to 1.

Answer 1

in that interval which would be the top and which would be bottom curve?

Answer 2

x^2 is on top

Answer 3

so do you remember how to use the integral to find area?

Answer 4

i think so

Answer 5

ok so what is it?

Answer 6

i would have (x^2-x^3)dx

Answer 7

exactly but what are the limits of integration?

Answer 8

and use the power rule of integration?

Answer 9

1 and 0 i believe

Answer 10

right, integral from 0 to one of (x^2 - x^3) dx

Answer 11

and use power rule like u said, and evaluate at those limits

Answer 12

do you know how to evaluate a definite integral?

Answer 13

and that becomes.. x^3/3-x^4/4

Answer 14

correct

Answer 15

and you plug in 1 and solve then 0 and solve

Answer 16

correct

Answer 17

but you subtract the x=0 evaluation form the x = 1 evaluation

Answer 18

1^3/3-1^4/4

Answer 19

but the x=0 evaluation is just 0 so you dont need to worry about it in this case

Answer 20

and you subtract 0^3/3-0^4/4 from that?

Answer 21

yea so it is then just 1/3-1/4

Answer 22

correct sir

Answer 23

which gives you 1/12?

Answer 24

correct

Answer 25

ok but in the back of my textbook its telling me it is .083

Answer 26

that why im confused

Answer 27

1/12 is approximately, .083

Answer 28

on a calculator put in 1/12

Answer 29

wow...

Answer 30

duhh lol

Answer 31

hehe

Answer 32

thank you very much

Answer 33

yw

Answer 34

u did all the work :)

Answer 35

well im glad i got to double check! lol

Answer 36

haha yeah

Answer 37

thanks again