This is because as the limits of integration approach infinity, the area under the curve becomes infinite. However, this infinity is balanced out by the infinitely small intervals of integration, resulting in a net value of zero.
Yes, it is possible for an integral to have non-zero values at the limits but still equal zero as the limits approach infinity. This is because the values at the limits may cancel each other out, resulting in a net value of zero.
No, the type of curve being integrated does not affect the result of the integral equaling zero as the limits approach infinity. This is because the concept of infinitely small intervals and balancing out of infinity still applies regardless of the shape of the curve.
Yes, there are some cases where the integral may not equal zero as the limits approach infinity. This can happen if the function being integrated is not continuous or if the limits of integration are not finite.
Yes, the result of an integral equaling zero as the limits approach infinity can be used to determine convergence or divergence of a series. This is because the integral test uses the concept of the integral equaling zero to determine the convergence or divergence of series. However, this is not the only method and there are other tests that can be used as well.