Problem
14. [-/1 Points] DETAILS SCALC9 4.4.027. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Evaluate the definite integral. \[ \int_{0}^{2}(2 x-6)\left(4 x^{2}+3\right) d x \] Need Help? Read It Watch It Submit Answer
Solution
Step 1 ：The given function is \((2x-6)(4x^2+3)\).
Step 2 ：Expand the function to get \(8x^3 - 24x^2 + 6x - 18\).
Step 3 ：Integrate each term separately to get \(2x^4 - 8x^3 + 3x^2 - 18x\).
Step 4 ：Substitute the upper and lower limits of the integral (2 and 0) into the integrated function and subtract the two results to get the final answer.
Step 5 ：The definite integral of the function \((2x-6)(4x^2+3)\) from 0 to 2 is \(\boxed{-56}\).
