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- anonymous

Suppose that f(x) is an EVEN function and let the integral f(x) dx from 0 to 1=5 and the integral f(x) dx from 0 to 7 =1. What is the integral from f(x) dx from -7 to -1?

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- anonymous

- katieb

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- myininaya

think if we have the integral of x^2 from -2..2 =16/3
if we have the integral of x^2 from 0..2=8/3
if we have the integral of x^2 from -2..0=8/3
so lets think about your problem

- anonymous

Since it's even, the integral from -7 to -1 is the same as the integral from 1 to 7.

- myininaya

right

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- myininaya

think about x^2
from 0..1, its 1/3
from 0..7. its 7^3/3
from -1..7 its 7^3/3+1/3

- myininaya

that last one is suppose to say -1..-7

- anonymous

is it negative -4

- myininaya

no what happen to x^2?

- myininaya

if you see what happen to x^2, you can see what will happen here

- myininaya

oh wait sorry i messed up on that last integral you might be right lol

- anonymous

Oh sorry I was figuring out the problem but you you would just flip the parameters and change the signs around right!

- myininaya

-4 u r right lol

- myininaya

from -7..-1 of x^2 its -1/3+7^3/3 to get this without integrating we just do 7^3/3-1/3 which is the integral from 0..7 minus the integral from 0..1

- anonymous

Okay I understand! So the integral from 1 to 0 f(x) dx = 5 changes to the integral from 0 to 1 f(x) dx = -5 and you add it to the integral from 0 to 7 which is 1 making -4

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