(a) The improper integrals
diverge and converge, respectively. Describe the essential difference between the integrands that cause one integral to converge and the other to diverge.
(b) Use a graphing utility to graph the function over the interval . Use your knowledge of the definite integral to make an inference as to whether the integral
converges. Give reasons for your answer.
(c) Use one application of integration by parts and the result of Exercise 89 to determine the divergence or convergence of the integral in part (b).
Laplace Transforms Let be a function defined for all positive values of t. The Laplace Transform of is defined by
If the integrands and causes an integral to converge and the other to diverge. Explain the differences between the two integrands.
The integrand in convergent. And the integrand is divergent
The following limit must exist to check for convergence;
The integrand on solving gives,
The integrand on solving gives:
It is found that,
To graph: The function is convergent or not overaninterval .
To calculate: The Convergence of integrand using by parts.
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