Question Detail
Question
Given k is a positive constant and ∫₂ᵇ (3eˣ+6e⁻²ˣ) dx = 0, find the value of b
Correct Answer
Option D is the correct answer.
Detailed Explanation
The antiderivative is 3eˣ-3e⁻²ˣ. Setting the definite integral from 2 to b equal to 0 means the antiderivative has the same value at both endpoints; b=2 trivially satisfies this since the interval collapses to zero width.
Hint
Set the antiderivative evaluated at b equal to its value at 2, since the definite integral is zero.