Definite Integration
Variable Limits Differentiation
Grade 12
Question:
<p>If <span>\(x\)</span> satisfies the equation <span>\(\int_x^{2x} \frac{1 + t^2 \sin^2 t}{t^2} dt = ...\)</span>, then</p>
<p>(A) 3</p>
<p>(B) –4</p>
<p>(C) 2</p>
<p>(D) 4</p>
Step-by-Step Solution
Key Concept: Apply Leibniz rule for differentiation of integrals with variable limits and solve for the parameter.
<p>This problem requires differentiating under the integral sign (Leibniz rule) and solving the resulting equation for <span>$x$</span>.</p>
Correct Answer: D