Question

use symmetry to evaluate the integral \[\int\limits_{-2}^{2}(3x ^{8}-2)dx\]

Answer 1

its an even function
you can change the integral into
2 * integral( 3x^8 - 2) dx where now limits change from 0 to 2

Answer 2

the whole function or just the 3x^8 part?

Answer 3

it doesn't matter, whole function is even as well as 3x^8 is even since f(x) = f(-x)

Answer 4

oh thanks. I see where I made the mistake in my problem.

Answer 5

glad to help