Question

The positive value of \( x \) satisfying the equation \[ \int_0^x (1 - t) \, dt = \frac{1}{2} \] is:

• A. 1
• B. \( \sqrt{2} \)
• C. 3
• D. 2

Hint:

For solving equations with definite integrals, evaluate the integral first, then solve the resulting equation for the unknown variable.

Answer 1

The Correct Option is D

We are given the integral equation: \[ \int_0^x (1 - t) \, dt = \frac{1}{2} \] By solving this definite integral and finding the value of \( x \) that satisfies the equation, we find that \( x = 2 \). Thus, the correct answer is option (4).