Question

Evaluate the integral using the properties of even and odd functions as an aid.

Answer 1

\[\int\limits_{-2}^{2} x ^{2}+1)dx\]

Answer 2

\(\Huge =2\int_0^2 (x^2+1)\) because x^2+1 is an even function

Answer 3

I forgot the dx

Answer 4

alright I know the answer for this is 272/15 but how do you do this Im new to this

Answer 5

well, it depends. there are a few ways to find this integral (power rule, limits, etc), and to know how to help you I need to know what course you are in. Are you currently in a pre-calc class covering basics of calculus, or is this a fully fledged calculus class?

Answer 6

No i'm in Calculus AB

Answer 7

the integral of x^2+1 is x^3/3+x+c

Answer 8

What confused is how come there is 3?

Answer 9

do you add the power?

Answer 10

by 1

Answer 11

Dude, shouldn't you be in the middle of the year of a calculus AB class?

Answer 12

Yea!

Answer 13

I'm pretty sure you should've learned this a while back...

Answer 14

My teacher is making me confused... he just recently!

Answer 15

the integral of \(x^n\) is \(\large \frac{x^{n+1}}{n}\)

Answer 16

+C of course

Answer 17

Yea I know that part!

Answer 18

that is a basic rule you should know. Apply it to what you have.

Answer 19

I'm confused with even and odd that's all

Answer 20

what's the integral of x^3+1?

Answer 21

do you know what an even and odd function is?

Answer 22

No

Answer 23

Can you explain to me please?

Answer 24

an odd function is a function such that f(-x)=-f(x). An even function is a function such that f(-x)=f(x). Graphically an even function is symmetrical about the y-axis while an odd function is symmetrical when rotated about the origin 180 degrees. Sin(x) is an odd function while cos(x) is an even function. using the laws of definite integrals, you can break up the integrals. If you know a function is odd, and say have to find the deifnite integral from -10 to 10, you know it is the same thing as finding the integral from 0 to 10 and multiplying by two.

Answer 25

THANKS!!!

Answer 26

read http://www.purplemath.com/modules/fcnnot3.htm for more information. Note that because you can "fold" the first picture they gave you in half (it's an even function), you only have to find the area of the right half of the parabola to find the area of the left half of the parabola

Answer 27

Oh Thanks! :)

Answer 28

Now I remember what my teacher means to say.