Question

If \(\int _1^a(2x+1)dx = 5\), then the sum of the values of \(a\) is..

• A. \(1\)
• B. \(-1\)
• C. \(7\)
• D. \(-7\)

Hint:

Evaluate the integral and use the sum of roots of the quadratic.

Answer 1

The Correct Option is B

Step 1: Solve the quadratic
$a=\frac{-1\pm\sqrt{29}}{2}$. Adding the two values: $\frac{-1+\sqrt{29}}{2}+\frac{-1-\sqrt{29}}{2}=-1$.

Final Answer:
Option (B). \[ \boxed{\text{(B)}} \]