Definite Integration
Radical Functions
Grade 12
Question:
<p>Value of \(\int_1^5 \{x + 2\sqrt{x-1} + \sqrt{x-2}(x-1)\} dx\) is</p>
<p>(a) \(\frac{8}{3}\)</p>
<p>(b) \(\frac{16}{3}\)</p>
<p>(c) \(\frac{32}{3}\)</p>
<p>(d) \(\frac{34}{3}\)</p>
Step-by-Step Solution
Key Concept: Break the integrand into separate terms and use substitution for each radical expression.
<p>Evaluate each term separately. Use appropriate substitutions for radical expressions. The sum of individual integrals yields $\frac{34}{3}$.</p>
Correct Answer: D