Integrate the function y = 3x\(^2\) + 2x - 5 with respect to x.
A
x\(^3\) + x\(^2\) - 5x + C
B
x\(^2\) + 2x\(^2\) - 5x + C
C
x\(^2\) + 2x - 5 + C
D
x\(^3\) + 2x - 5 + C
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
∫ (3x² + 2x - 5) dx
= ∫ 3x² dx + ∫ 2x dx + ∫ (-5) dx
= 3 · (\(\frac{x^3}{3}\)) + 2 · (\(\frac{x^2}{2}\)) + (-5) · x + C
= x\(^3\) + x\(^2\) - 5x + C
Source: WAEC / JAMB / NECO Classroom Archive (Record #74191)