Am I solve correct? Please help.

[xiaoyu]

Hi everyone. I am trying the solve this question. I made a solution but I am not pretty sure it is correct. Can you help me?

 

[Deleted member 4993]

Hi everyone. I am trying the solve this question. I made a solution but I am not pretty sure it is correct. Can you help me?

I see two problems - however those cancelled each other and your answer may be correct.

The limits of integrations are incorrect. Draw an approximate sketch of the graphs of the functions and you'll see that:

the limits on 'y' goes from y = x² (lower limit) to y = -x, and,​

​

the limits on 'x' goes from 0 to (-1)​

 

[xiaoyu]

I see two problems - however those cancelled each other and your answer may be correct.

The limits of integrations are incorrect. Draw an approximate sketch of the graphs of the functions and you'll see that:

the limits on 'y' goes from y = x² (lower limit) to y = -x, and,​

​

the limits on 'x' goes from 0 to (-1)​

Thanks for your answer. One more question, limit x goes from 0 to (-1) you said but in the question I see 1 instead of -1. What is the reason?

 

[tkhunny]

Besides the magically cancelling errors, you lost the "3" you started with. Don't do that.

 

[Dr.Peterson]

I see no wrong limits of integration, only the dropped 3.

I think SK misread [MATH]x\ge 0[/MATH].

 

[xiaoyu]

I see no wrong limits of integration, only the dropped 3.

I think SK misread [MATH]x\ge 0[/MATH].

3 disappear because of the first integration part. I mean I thought like that when I delete. If I'm include the 3, 3 in the denominators will disappear. Result will change. Am I understand correctly?

 

[Steven G]

I see two problems - however those cancelled each other and your answer may be correct.

The limits of integrations are incorrect. Draw an approximate sketch of the graphs of the functions and you'll see that:

the limits on 'y' goes from y = x² (lower limit) to y = -x, and,​

​

the limits on 'x' goes from 0 to (-1)​

You might as well move into the corner at this rate. You found two errors? Oh boy. I think that you need to view some of Sal's videos.

 

[tkhunny]

3/3 = 1 -- That's the idea. Leads to x^7 +x^4 heading into the second integration.

The integration limits are not wrong, per se, they are just written unconventionally there in the middle. No matter, though, since they were subsequently used as if they had been written conventionally.

 

[Steven G]

3/3 = 1. Where are you confused? Please post back. Thank you.

 

[xiaoyu]

I solved again. I hope this one is correct. Thank you for your help.

 

[Deleted member 4993]

Thanks for your answer. One more question, limit x goes from 0 to (-1) you said but in the question I see 1 instead of -1. What is the reason?

Yes I missed the part about the boundary being x≤0 and x = 1.

The correct limits should be:

the limits on 'y' goes from y = -x (lower limit) to y = x²(upper limit), and,​

​

the limits on 'x' goes from 0 to (1)​

I "somehow" thought that the limits are the points of intersections [(0,0) and (-1,1)] - corner time as Jomo had suggested.