Final answer:
To evaluate the definite integral, the integrand (2e^8x - 3)/(e^4x) is simplified and integrated term by term, then evaluated at the bounds of integration to obtain the total area, which represents the value of the definite integral.
Step-by-step explanation:
The student has asked to evaluate the definite integral of (2e^8x - 3)/(e^4x) from 0 to 1. To solve this, we can simplify the integrand by dividing each term in the numerator by e4x, which results in the integral of 2eT4x - 3eT-4x from 0 to 1. We can then integrate each term separately.
Integrating 2e^4x gives us (1/2)e^4x and integrating -3e^-x gives us (3/4)e^-4x. After integrating, we evaluate each term at the upper and lower bounds and find the difference.
The final step is to substitute the limits into the integrated expression and subtract the evaluated expression at the upper limit from the evaluated expression at the lower limit to get the total area under the curve, which is the value of the definite integral.