Question:medium

Given \(\int_1^a (2x + 1) \, dx = 5\), find the sum of all values of \(a\).

Show Hint

When a question asks for the "sum of all values" of a variable resulting from a quadratic equation, do not waste time finding individual roots (using the discriminant). Use the sum of roots formula \(-B/A\) directly!

Updated On: Apr 11, 2026

Show Solution

Solution and Explanation

Was this answer helpful?

Questions Asked in MHT CET exam

Find the heat energy that must be supplied to 14 g of nitrogen at room temperature to raise its temperature by \(48^\circ\text{C}\) at constant pressure. (Molecular weight of nitrogen = 28; \(R\) is the gas constant; \(C_p = \frac{7}{2}R\) for a diatomic gas.)

MHT CET - 2026
Thermodynamics

View Solution

If \(y = f\left(\frac{3 + 2x}{3 - 2x}\right)\), where \(f(x) = \tan(\log x)\), and \(\frac{dy}{dx} = \frac{A}{B + Cx^2} \cdot \sec^2\left(\log \frac{3 + 2x}{3 - 2x}\right)\), then find \(A, B, C\).

MHT CET - 2026
Coordinate Geometry

View Solution

A particle starts oscillating simple harmonically from its mean position with time period \(T\). At time \(t = \frac{T}{6}\), find the ratio of potential energy to kinetic energy of the particle.

MHT CET - 2026
Waves and Oscillations

View Solution

A plane is formed by the axes whose centroid is \(\left(2, -\frac{2}{3}, \frac{1}{2}\right)\). Find the distance of the plane from the origin.

MHT CET - 2026
Inverse Trigonometric Functions

View Solution

Given \(\int_1^a (2x + 1) \, dx = 5\), find the sum of all values of \(a\).

Show Hint

Solution and Explanation

Top Questions on Calculus

Questions Asked in MHT CET exam