Definite Integration
Area-Integral Interplay
Grade 12
Question:
<p>Evaluate \(\displaystyle\int_0^1(1-x)^{50}\,dx\). [JEE Advanced 2011]</p>
Step-by-Step Solution
Key Concept: Let t=1-x: \int_0^1 t^5^0 dt = 1/51.
<div class='solution'>
<p>$\int_0^1(1-x)^{50}dx\stackrel{t=1-x}{=}\int_0^1 t^{50}dt=\frac{1}{51}$</p>
Correct Answer: A