Question:
\(\int_0^1 x^{99} \, dx \)
\(\int_0^1 x^{99} \, dx \)
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For powers of \( x \), use the power rule: \( \int x^n \, dx = \frac{x^{n+1}}{n+1} \).
Updated On: Sep 13, 2025
- 100
- \( \frac{1}{100} \)
- 1
- 101
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The Correct Option is C
Solution and Explanation
We are given:
\[
I = \int_0^1 x^{99} \, dx
\]
Using the power rule for integration:
\[
I = \left[ \frac{x^{100}}{100} \right]_0^1 = \frac{1^{100}}{100} - \frac{0^{100}}{100} = \frac{1}{100}
\]
Thus, the correct answer is \( \frac{1}{100} \).
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