Evaluate: \(\int(2x + 1)^3 dx\)
FURTHER MATHEMATICS
WAEC 2023
Evaluate: \(\int(2x + 1)^3 dx\)
- A. \(8(2x + 1)^2 + k\)
- B. \(6(2x + 1)^2 + k\)
- C. \(\frac{1}{8} (2x + 1)^4 + k\)
- D. \(\frac{1}{6} (2x + 1)^4 + k\)
Correct Answer: C. \(\frac{1}{8} (2x + 1)^4 + k\)
Explanation
\(\int(2x + 1)^3 dx\)
Using substitution method, Let \(u = 2x + 1\)
\(\frac{du}{dx}=2==>du=2dx==>dx=\frac{du}{2}\)
=\(\int\frac{u^3}{2} du = \frac{1}{2}\int u^3 du\)
=\(\frac{1}{2}(\frac{u^4}{4})=\frac{u^4}{8}\)
\(\therefore\frac{1}{8} (2x + 1)^4 + k\)
Post an Explanation Or Report an Error
If you see any wrong question or answer, please leave a comment below and we'll take a look. If you doubt why the selected answer is correct or need additional more details? Please drop a comment or Contact us directly. Your email address will not be published. Required fields are marked *