Question

\(\int_0^1 x^{99} \, dx \)

• A. 100
• B. \( \frac{1}{100} \)
• C. 1
• D. 101

Hint:

For powers of \( x \), use the power rule: \( \int x^n \, dx = \frac{x^{n+1}}{n+1} \).

Answer 1

The Correct Option is C

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 \( \frac{1}{100} \).