Question

The correct option is ∫f(x² - 6x 5) dx = ∫(x - 1)² dx, and the evaluation yields : (applying the power rule for integration.)

A) 1/3 (x−1)^3 +C, where C is the constant of integration.
B) 1/3 (x−1)^3+5x+C, where C is the constant of integration.
C) 1/3 (x−1)^3−5x+C, where C is the constant of integration.
D) 1/3 (x−1)^3+6x+C, where C is the constant of integration.

Answer 1

The integral of (x - 1)² dx is evaluated using the power rule for integration, resulting in 1/3 (x-1)³ + C, where C is the constant of integration.

Step-by-step explanation:

The integral in question is ∫f(x² - 6x + 5) dx, which is equivalent to the integral of (x - 1)² dx. To solve this, we apply the power rule for integration. The integral of (x - 1)² dx is given by ∫(x - 1)² dx = 1/3 (x - 1)³ + C, where C is the constant of integration. Therefore, the correct evaluation of the integral is 1/3 (x−1)³ + C.