Exercise
$\int_{\frac{1}{2}}^{\infty}\left(\frac{4x^2-3}{e^2}\right)dx$
Step-by-step Solution
Learn how to solve problems step by step online. Integrate the function (4x^2-3)/(e^2) from 1/2 to infinity. Take the constant \frac{1}{e^2} out of the integral. Expand the integral \int\left(4x^2-3\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. Solve the product \frac{1}{e^2}\left(\int4x^2dx+\int-3dx\right). The integral \frac{1}{e^2}\int4x^2dx results in: \frac{4x^{3}}{3e^2}.
Integrate the function (4x^2-3)/(e^2) from 1/2 to infinity
Final answer to the exercise
The integral diverges.