"Of those I looked at, all had Chinese authors. "

I agree with you and I too felt strange about this.
But I don't think this English term was invented by the Chinese.

"Of those I looked at, all had Chinese authors. "

I agree with you and I too felt strange about this.
But I don't think this English term was invented by the Chinese.

Is the integral of (ax^2 + bx + c), from -5 to 5, equal to twice the integral of (ax^2 + c), from 0 to 5?


Consider the odevity of the functions.

(1) Since b*x is an odd function,  int(b*x,x=-5..5)=0.
(2) Since a*x^2+c is an even function, int(a*x^2+c,x=-5..5)=2*int(a*x^2+c,x=0..5).

Is the integral of (ax^2 + bx + c), from -5 to 5, equal to twice the integral of (ax^2 + c), from 0 to 5?


Consider the odevity of the functions.

(1) Since b*x is an odd function,  int(b*x,x=-5..5)=0.
(2) Since a*x^2+c is an even function, int(a*x^2+c,x=-5..5)=2*int(a*x^2+c,x=0..5).

Thanks for the helpful information.

Thanks for the helpful information.

Yes, both work very well in Maple 8.
So my problem is completely solved.
Thank you very much.

plot(surd(x,3),x=-2..2,thickness=3);
with(plots): a:=1:
implicitplot(surd(x^2,3)+surd(y^2,3)=a^(2/3),x=-a..a,y=-a..a);

Yes, both work very well in Maple 8.
So my problem is completely solved.
Thank you very much.

plot(surd(x,3),x=-2..2,thickness=3);
with(plots): a:=1:
implicitplot(surd(x^2,3)+surd(y^2,3)=a^(2/3),x=-a..a,y=-a..a);

Thank you, acer.

Using surd (which I don't know before) in Maple 8 can solve the second problem by the following code (which can produce the whole graph):
 

with(plots):
plot(surd(x,3),x=-1..1);

Thank you, acer.

Using surd (which I don't know before) in Maple 8 can solve the second problem by the following code (which can produce the whole graph):
 

with(plots):
plot(surd(x,3),x=-1..1);

Thanks. But how can I solve the problem in Maple 8?
It seems that Maple does not allow power functions with fractional powers or decimal powers to take negative values  even if they are defined there like y=x^(1/3)..

Thanks. But how can I solve the problem in Maple 8?
It seems that Maple does not allow power functions with fractional powers or decimal powers to take negative values  even if they are defined there like y=x^(1/3)..

" the numpoints option just gives the plot routine a minimum for the number of points"

This made me better understand the meaning of the adaptive option. Thank you, Scott.

" the numpoints option just gives the plot routine a minimum for the number of points"

This made me better understand the meaning of the adaptive option. Thank you, Scott.

Thank you for your help. Your code is much simpler. Just  by controlling the number of points of a circle!

with(plots):
with(plottools):
R:=2:N:=7:
C:=circle([0,0],R,color=red):
P:=polarplot(R,Pi/2..2*Pi,numpoints=N+1,adaptive=false,colour=blue):
display(C,P,thickness=3);


What does adaptive=false mean here? Thanks again.