Definite Integration
Area-Integral Interplay
Grade None
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.
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<p>$\int_0^1(1-x)^{50}dx\stackrel{t=1-x}{=}\int_0^1 t^{50}dt=\frac{1}{51}$</p>
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Correct Answer: A