Let f(t) be a function defined for all positive values of t. the laplace transform of f(t) is defined by the following integral, if the improper integral exists. f(s) = ∞e−st f(t) dt0 laplace transforms are used to solve differential equations. find the laplace transform of the function. f(t) = cos at

We have laplace transform of any function is defined as

thus for

Now integrating the given expression using the integration by parts principle we have

Note that we get the first integral back in the RHS expression

Thus solving we have

Solving for I we get

now applying the limits we have

triangle and cube

step-by-step explanation: