Question

The integral $ \int (3x^2 - 2x + 1) \, dx $ is:

• A. $ x^3 - x^2 + x + C $
• B. $ x^3 - x^2 - x + C $
• C. $ x^3 + x^2 + x + C $
• D. $ 3x^3 - 2x^2 + x + C $

Hint:

When integrating polynomials, apply the power rule individually to each term.

Answer 1

The Correct Option is A

Integrate term by term: $$ \int (3x^2 - 2x + 1) \, dx = \int 3x^2 \, dx - \int 2x \, dx + \int 1 \, dx $$
Apply power rule to each: $$ \int 3x^2 \, dx = x^3,\quad \int -2x \, dx = -x^2,\quad \int 1 \, dx = x $$
Combine results and add constant of integration $ C $: $$ \int (3x^2 - 2x + 1) \, dx = x^3 - x^2 + x + C $$