Final answer:
To evaluate the given definite integral from 1 to x2, expand and integrate term-by-term, multiplying each term by 9, and then substitute the limits to find the area under the curve.
Step-by-step explanation:
The definite integral of a function represents the area under the curve of the function between two points on the x-axis. To evaluate the integral ∫(9(x² - 4x + 6)) dx from 1 to an unspecified upper limit, we first express the integral in a simplified form. This involves expanding the equation within the integral and then integrating term-by-term.
First, we multiply out the constant: ∫9*(x² - 4x + 6)dx = 9*∫(x² - 4x + 6)dx.
Next, we integrate the function term-by-term from 1 to the unspecified upper limit x2:
- Integrate x² to get (1/3)x³.
- Integrate -4x to get -2x².
- Integrate 6 to get 6x.
After integrating, we multiply each term by 9 to get: 9[(1/3)x³ - 2x² + 6x]. We evaluate this from x = 1 to x = x2, and calculate the final value by substituting the upper and lower limits into the integrated function and finding the difference.