Question

Evaluate \(\rm \int (x-2)(x-3)dx\)
1. \(\rm \frac{x^3}{3} - \frac{5x^2}{2}+6x +c\)
2. \(\rm \frac{x^3}{3} + \frac{5x^2}{2}+6x +c\)
3. \(\rm \frac{x^2}{3} + \frac{5x^2}{2}-6x +c\)
4. None of the above 

Answer 1

Correct Answer - Option 1 : \(\rm \frac{x^3}{3} - \frac{5x^2}{2}+6x +c\)

Concept:

\(\rm \int x^n dx = \frac{x^{n+1}}{n+1}+c\)

Calculation:

I = \(\rm \int (x-2)(x-3)dx\)

= \(\rm \int (x^2-2x - 3x + 6)dx\)

= \(\rm \int (x^2-5x + 6)dx\)

= \(\rm \frac{x^3}{3} - \frac{5x^2}{2}+6x +c\)