Evaluate; \(\int^3_1(3x - 2)^5 dx\)
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Correct Answer: Option
Explanation:
\(\int^3_1(3x - 2)^5 dx\)
Let u = 3x - 2
\(\frac{du}{dx}\) = 3
dx = \(\frac{dy}{3}\)
\(\int^3_1(3x - 2)^5 dx\) = \(\int^7_1 \frac{u^5}{3} du\)
= \(\frac{u^{5 + 1}}{3(5 + 1)}|^7_1\)
= \(\frac{u^5}{18}|^7_1\)
= \(\frac{7^6}{18} = \frac{1^6}{18}\)
= \(\frac{7^6 - 1}{18}\)
= \(\frac{117649}{18}\)
= 6536
\(\int^3_1(3x - 2)^5 dx\)
Let u = 3x - 2
\(\frac{du}{dx}\) = 3
dx = \(\frac{dy}{3}\)
\(\int^3_1(3x - 2)^5 dx\) = \(\int^7_1 \frac{u^5}{3} du\)
= \(\frac{u^{5 + 1}}{3(5 + 1)}|^7_1\)
= \(\frac{u^5}{18}|^7_1\)
= \(\frac{7^6}{18} = \frac{1^6}{18}\)
= \(\frac{7^6 - 1}{18}\)
= \(\frac{117649}{18}\)
= 6536