Question

\(3\displaystyle \int_{0}^{3} x^{3}\,dx=\) ?

• A. \(\dfrac{81}{4}\)
• B. \(\dfrac{243}{4}\)
• C. \(0\)
• D. \(\dfrac{9}{4}\)

Hint:

Do the definite integral first, then multiply by outside constants.

Answer 1

The Correct Option is B

\(\int x^{3}dx=\dfrac{x^{4}}{4}\). Evaluate from \(0\) to \(3\): \[ \left[\frac{x^{4}}{4}\right]_{0}^{3}=\frac{3^{4}}{4}-0=\frac{81}{4}. \] Multiply by \(3\): \(3\cdot\dfrac{81}{4}=\dfrac{243}{4}\).