Question

how do you know when you need to flip the limits of integration?

Answer 1

When the lower bound is greater than the upper bound.

Answer 2

\[\int\limits_{10}^{0}f(x)dx = - \int\limits_{0}^{10}f(x)dx\]

Answer 3

I think that's the property.

Answer 4

can you be more specific with this question? Do you have a particular problem ?

Answer 5

so if I have 6 on the top and x on the bottom then I don't have to flip it?

Answer 6

Are you referring to the fundamental theorem of calculus part I?

Answer 7

so if I have 6 on the top and x on the bottom then I don't have to flip it?\[\int\limits_{x}^{6}\cos(\sqrt{s ^{4+1}}) ds\]

Answer 8

here is the exact problem. yes. i am

Answer 9

Yes, you need to flip the bounds, because by the FToC, it requires that the lower limit to be a constant and the upper limit to be the variable

Answer 10

use that property of definite integrals to switch the limits and add a "\(-\)" in front of the integral

Answer 11

ok so if my lower limit was 2 and upper limit was a variable of 2x+1 then I don't need to switch right?

Answer 12

You got it.

Answer 13

thanks!