integration Q (1 Viewer)

[ToO LaZy ^*]

int[pi/4 -> -pi/4] (x³ / cos(x) )dx

i'm not sure how these odd/even functions work..?..we weren't taught them.

the answer to the above = 0, but i don't understand their working..

 

[wogboy]

If f(x) is odd, Integral{-a -> a} f(x) dx = 0 (for all a)
If f(x) is even, Integral{-a -> a} f(x) dx = 2*Integral{0 -> a} f(x) dx (for all a)

f(x) = (x^3)/(cosx) is an odd function ...

 

[Xayma]

Think of an odd function, it is reflected along the line y=-x.

So if you are taking an area (a --> -a) then any positive area is cancelled out by any negative area that is created by the reflection.

 

[ToO LaZy ^*]

how do you find out if the function is odd or even?

top f(x) / bottom f(x)..?

 

[Xayma]

A function is odd if f(-x)=-f(x)
A function is even if f(-x)=f(x)

Sine is an odd function.
Tan is an odd function.
Cos is an even function.

A polynomial is even if it only contains even degrees (and a constant)
A polynomial is odd if it only contains odd degrees (no constant)

 

[ToO LaZy ^*]

ohhhhhhhhhhh...i remember now.
thx !

 

[shkspeare]

wtf u do 4unit and u didnt know how to do odd/even functions????

 

[CrashOveride]

That was a bit harsh shakespeare, especially for a man of your character

 

[ToO LaZy ^*]

erm..i forgot