Question:
\(3\displaystyle \int_{0}^{3} x^{3}\,dx=\) ?
\(3\displaystyle \int_{0}^{3} x^{3}\,dx=\) ?
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Do the definite integral first, then multiply by outside constants.
Updated On: Oct 17, 2025
- \(\dfrac{81}{4}\)
- \(\dfrac{243}{4}\)
- \(0\)
- \(\dfrac{9}{4}\)
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The Correct Option is B
Solution and Explanation
\(\int x^{3}dx=\dfrac{x^{4}}{4}\).
Evaluate from \(0\) to \(3\):
\[
\left[\frac{x^{4}}{4}\right]_{0}^{3}=\frac{3^{4}}{4}-0=\frac{81}{4}.
\]
Multiply by \(3\): \(3\cdot\dfrac{81}{4}=\dfrac{243}{4}\).
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