Question

Find the general integral

Answer 1

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

Answer 2

can you tell me whether 1/x^2 is an even function or odd function ?

Answer 3

not to sure what you mean

Answer 4

let f(x) = 1/x^2
Find f(-x)
by replacing x in f(x) by -x.
If f(-x) = f(x), then the function is even
If f(-x) = -f(x), then the function is odd
else neither.

Answer 5

i am asking you this, because we can use the property of definite integrals,
\(\int \limits_{-a}^af(x)dx = 0 \\ \text{if the function f(x)is odd, } \\\int \limits_{-a}^af(x)dx = 2\int \limits_{0}^af(x)dx \\ \text{if the function f(x)is even.} \)

Answer 6

did you know this property ?

Answer 7

if you didn't know it,
you can use the general formula for integration
\(\int x^ndx= x^{n+1}/(n+1)+c\)
because 1/x^2 can be written as x^{-2}

Answer 8

the integral is improper as well