Definite Integration
Properties of Definite Integrals
Grade 12

Question:

<p>\(100\int_0^1 \{x\} dx\), where \(\{x\}\) denotes the fractional part of \(x\)</p>
<p>(a) 100</p>
<p>(b) 25</p>
<p>(c) 75</p>
<p>(d) 50</p>

Step-by-Step Solution

Key Concept: The fractional part function equals the identity function on [0,1), allowing direct integration.
<p>For $x \in [0,1)$, $\{x\} = x$. Therefore, $\int_0^1 \{x\} dx = \int_0^1 x dx = \frac{x^2}{2}\big|_0^1 = \frac{1}{2}$. Thus $100 \times \frac{1}{2} = 50$.</p>
Correct Answer: D

Master Definite Integration with Mathbee

Practice this topic under real exam conditions with strict timers, or ask our AI Mentor to explain the concepts step-by-step.

Start Practicing for Free