14. [-/1 Points] DETAILS SCALC9 4.4.027.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Evaluate the definite integral.
\[
\int_{0}^{2}(2 x-6)\left(4 x^{2}+3\right) d x
\]
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Answer

The definite integral of the function \((2x-6)(4x^2+3)\) from 0 to 2 is \(\boxed{-56}\).

Steps

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 \(\boxed{-56}\).

14. [-/1 Points] DETAILS SCALC9 4.4.027.MY NOTESASK YOUR TEACHERPRACTICE ANOTHEREvaluate the definite integral.\[\int_{0}^{2}(2 x-6)\left(4 x^{2}+3\right) d x\]Need Help?Read ItWatch ItSubmit Answer

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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