Final answer:
To evaluate the given integral, we can use integration by parts. By defining u = sin(2x) and dv = e^-3x dx, we can apply the tabular method and set up a table to find du and v. Using the integration by parts formula, we can then plug in the values from the table and simplify the integral.
Step-by-step explanation:
To evaluate the integral ∫ e-3xsin(2x) dx using the tabular method, we need to use integration by parts. Let's define u = sin(2x) and dv = e-3x dx. Then, we can find du and v by differentiating and integrating respectively.
Using the tabular method, we can set up the table as follows:
udvduvsin(2x)e-3x dx2cos(2x) dx-1/3e-3x
Next, we can apply the integration by parts formula:
∫ u dv = uv - ∫ v du
Plugging in the values from the table:
∫ e-3xsin(2x) dx = -1/3e-3xsin(2x) - ∫ -1/3e-3x2cos(2x) dx
Simplifying the integral on the right-hand side, we can further solve it using the tabular method or directly integrate.
Remember to evaluate the definite integral if a specific interval is given.