Find ∫(x2 + 3x − 5)dx
A
\(\frac{x_3}{3}\) - \(\frac{3x_2}{2}\) - 5x + k
B
\(\frac{x_3}{3}\) - \(\frac{3x_2}{2}\) + 5x + k
C
\(\frac{x_3}{3}\) + \(\frac{3x_2}{2}\) - 5x + k
D
\(\frac{x_3}{3}\) + \(\frac{3x_2}{2}\) + 5x + k
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
∫xndx = \(\frac{x_{n + 1}}{n + 1}\)
∫dx = x + k
where k is constant
∫(x2 + 3x − 5)dx
∫x2 dx + ∫3xdx − ∫5dx
\(\frac{2_{2 + 1}}{2 + 1}\) + \(\frac{3x^{1 + 1}}{1 + 1}\) − 5x + k
\(\frac{x_3}{3}\) + \(\frac{3x_2}{2}\) − 5x + k
Source: Myschool Past Questions Archive (Record #46356)