Question

Evaluate the definite integral:

Answer 1

expand, then integrate term by term

also notice that this function is even, so we can make this integral a little simpler

Answer 2

So i went ahead and expanded the squared polynomial

Answer 3

here's what I got, which may not be correct:

Answer 4

did you know that for all even functions f(x) that are defined on the interval [-a,a] we have that\[\int_{-a}^af(x)dx=2\int_0^af(x)dx\]?
that may make the evaluation a lot easier

Answer 5

integrand from (-2) to (2) of x^4_2x^2+1 dx

Answer 6

oops x^4-2x^2+1 dx

Answer 7

and the integral of that is...?

Answer 8

well that's where I think I went wrong, because simplifying exponents, negatives, and fractions was a bit tough.. let me write it out

Answer 9

(1/5)x^5 - (2/3)x^3+x

Answer 10

looks good

Answer 11

@TuringTest so what your saying is that I should change the numbers to 2 and 0 because they are equal?

Answer 12

sorry i mean mult the integral by 2

Answer 13

no
there are rules about even and odd integrand over symmetric intervals

can you recognize that the integrand is even?

Answer 14

in this case yes, but you should understand why

Answer 15

ok. so if I did get the simplified version correct, if my answer is wrong it must be in the way i distributed out and simplified? my answer was 4, but that's not correct.

Answer 16

What is the order of operations again? exponents before fractions, right?

Answer 17

hmm... I though OS was shutting down

Answer 18

yes, exponents before fractions