Q88 / 150 · MHT CET 2026 (11 April Shift 1) · Mathematics
If $\int_1^a (2x + 1) dx = 5$, then the sum of the values of $a$ is..
- A$1$
- Correct answerB$-1$
- C$7$
- D$-7$
Solution
Evaluating the definite integral:
$\int_1^a (2x + 1) dx = [x^2 + x]_1^a$
Substituting the limits:
$(a^2 + a) - (1^2 + 1) = 5$
$a^2 + a - 2 = 5$
$a^2 + a - 7 = 0$
This is a quadratic equation in $a$. The sum of the roots of the equation is $-\dfrac{1}{1} = -1$.
Answer: $-1$
$\int_1^a (2x + 1) dx = [x^2 + x]_1^a$
Substituting the limits:
$(a^2 + a) - (1^2 + 1) = 5$
$a^2 + a - 2 = 5$
$a^2 + a - 7 = 0$
This is a quadratic equation in $a$. The sum of the roots of the equation is $-\dfrac{1}{1} = -1$.
Answer: $-1$
Hence, the correct answer is option: 'B'.