Question

Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative.) f(x) = (x + 3)(2x − 2)

Answer 1

Answer:

2x³/3 +2x²-6x+C

Step-by-step explanation:

Given the function

f(x) = (x + 3)(2x − 2)

Expand first

f(x) = 2x²-2x+6x-6

f(x) = 2x²+4x-6

Integrate the resulting function

Integrate (2x²+4x-6) =2x³/3 + 4x²/2 - 6x + C

= 2x³/3 +2x²-6x+C

For us to check the correctness, we need to differentiate the answer and we must arrive back at the question

On differentiating 2x³/3 +2x²-6x

3(2/3)x² + 2(2)x¹ -6

= 6/3x²+4x-6

= 2x²+4x-6

This shows the answer is correct.

The correct anti derivative of the function is 2x³/3 +2x²-6x+C