Definite Integration
Integration with GIF
Grade 12
Question:
<p>If <span>\([\cdot]\)</span> is G.I.F., then <span>\(\int_0^{10} \frac{[x^2]}{4[x^2 - 28x + 196] + [x^2]} dx\)</span> is</p>
<p>(A) 0</p>
<p>(B) 1</p>
<p>(C) 3</p>
<p>(D) 4</p>
Step-by-Step Solution
Key Concept: Recognize that the expression in the denominator involves a perfect square, and use properties of the greatest integer function to simplify.
<p>Evaluate using properties of the greatest integer function and observe that the denominator can be simplified using the fact that <span>$x^2 - 28x + 196 = (x-14)^2$</span>.</p>
Correct Answer: A