amistre64 5 years ago The Area of the region bounded by the x-axis and the graph of y= x^3-x: Is it: 1/2 ; 1/4 ; -1/4 ; 0

1. amistre64

... or other :)

2. anonymous

Doesn't look very well bounded to me :P

3. amistre64

Me either :)

4. amistre64

I thought if anything it was the interval between -1 and 1

5. anonymous

Which you could say the area is 1/2 total..

6. amistre64

that was my first conjecture as well.. But then I read one source that says odd functions cancel to zero; and others which say to add absolute values of the areas together

7. anonymous

You don't need a source to say odd functions cancel to zero :(

8. amistre64

lol..... I wish that was true :) but im just to much of an idiot at this stage to know the differences ;)

9. anonymous

:( If I asked you to find: $\int^\pi_{-\pi}x^{10} \sin x \mathbb{d}x$ would you do it all by parts?

10. amistre64

hmm... I would notice that the graph of the sine is odd and that the part [-pi,0] has the same "area" as [0,pi] and conclude that the total area would be both parts.

11. anonymous

:( The integral is 0 because the functions cancel. HOWEVER, from the exact phrasing of your question, I think you may have to add them together, rather than say 'they cancel', but not completely sure.

12. amistre64

I agree that the functions cancel. But intuitivly I want to say that the areas combine to total 1/2. But then the question leaves me to beleieve also that the "bounds" of the function are limitless and not just confined to an interval [-1,1]. The total area under the curve and bounded by the x axis would then be zero to me becasause I can t see trying to take an infinite area....

13. anonymous

I think in questions like this it is assumed they mean the 'finite area bounded' - it is just sometimes left out.

14. amistre64

I agree. But the solutions I put into the answer box all tell me im wrong. ......

15. anonymous

You tried all the solutions in your original post? Hmm

16. amistre64

yep, tried 1/2 to begin with; then figured if it aint that then zero, then the only other options that make sense are 1/4 or -1/4. I think the programs broke :)

17. anonymous

:(

18. amistre64

infinity/2...maybe? lol

19. anonymous

I honestly have no idea what it could be. I agree, it's broken.