Question

determine if convergent and divergent. prove. integral between -infinity and 6 for 10xe^2x dx

Answer 1

\[\int\limits_{-\infty}^{6} 10xe ^{2x}dx\]

Answer 2

have you tried using integration by parts yet

Answer 3

i can do an integration by parts. i just don't know the process to arrive to the conclusion of divergence or convergence..... it is from the chapter of improper integrals.

Answer 4

well we can do integration by parts and then apply the limits to find whether or not the integral converges or not

Answer 5

I guess I will assume you did the integration by parts....
\[\lim_{z \rightarrow - \infty }[ 5x e^{2x}-\frac{5}{2}e^{2x}]_{z}^{6}\]
plug in upper and lower limit just like you would if you were evaluating a definite integral

Answer 6

then evaluate the limit

Answer 7

if the limit is a number then it converges
if the limit is not a number then it diverges

Answer 8

and yes -inf and inf are not numbers

Answer 9

cool thanks. got it