Question

If ∫1[infinity]F(X)Dx Converges,

Then ∫0[infinity]F(X)Dx Converges Also.
a true
b false

Answer 1

The statement is false. The convergence of an integral from 1 to infinity does not guarantee the convergence of the integral from 0 to infinity.

Step-by-step explanation:

The statement is false. If the improper integral ∫1∞F(x)dx converges, it means that the area under the curve of F(x) from 1 to infinity is finite. However, the integral ∫0∞F(x)dx includes the area from 0 to 1 in addition to the area from 1 to infinity, making it larger than the previous integral. Therefore, the integral ∫0∞F(x)dx may or may not converge, depending on the behavior of F(x) between 0 and 1.