int. qn.. (1 Viewer)

[bos1234]

Using the properties of the definite integral explain why:

a
| (ax^5+bx^4 + cx^3 + dx^2 + ex + f)dx =.................a
-a ................................................................................2|(bx^4 + dx^2 + f)dx
....................................................................................0



|
-
is the integration sign... and d.w about the full stops..

so its

int. up lim. a lower lim -a... = int up lim a.. lower lim 0

 

[acmilan]

ax^5 + cx^3 + ex is odd, so integrating from -a to a gives 0

bx^4 + dx^2 + f is even, so integrating from -a to a is the same as twice the integral from 0 to a

 

[bos1234]

ok thanks got it!

 

[Slidey]

Please don't delete your threads after you've been given the answer. They pften are useful for others to read.

 

[bos1234]

kk sry man

 

[davidw89]

ax^5 + cx^3 + ex is odd, so integrating from -a to a gives 0

bx^4 + dx^2 + f is even, so integrating from -a to a is the same as twice the integral from 0 to a

how do u actually set it out though

 

[pLuvia]

how do u actually set it out though

You don't have to, it's a given. Take a look at the curve f(x)=x³ this is an odd function, if I integrate between -1 and 1, I will obtain 0, try it. Or you could simply observe and see that the area of the 1st quad is equal to the area of the 3rd quad but since the 3rd quad is negative hence -ve plus +ve=0

With even functions i.e. f(x)=x² it is symmetrical about the y axis hence integrating from -1 to 1 is equal to integrating from 0 to 1 (or -1 to 0) doubled