Evaluate; \(\int^3_1(3x - 2)^5 dx\)
Question 1 Report
Evaluate; \(\int^3_1(3x - 2)^5 dx\)
Answer Details
Integrate \( (3x - 2)^5 \) by reversing the chain rule (raise the power, divide by the new power and by the derivative of the bracket, \(3\)):
\[ \int (3x - 2)^5\,dx = \frac{(3x - 2)^6}{6 \times 3} = \frac{(3x - 2)^6}{18}. \]
Evaluate between \(1\) and \(3\):
\[ \left[\frac{(3x - 2)^6}{18}\right]_1^3 = \frac{(7)^6}{18} - \frac{(1)^6}{18} = \frac{117649 - 1}{18} = \frac{117648}{18} = 6536. \]
The value of the integral is \( 6536 \).
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