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Calculus Level 5

Find the value of $\displaystyle \lim_{x\to 0}\left(\int_{0} ^{1}(by+a(1-y))^{x}.dy\right)^{\frac{1}{x}}$ where $b>a$ .

\frac{1}{e}.(\frac{b^{b}}{a^{a}})^{\frac{1}{b-a}}

\frac{1}{e}.(\frac{a^{a}}{b^{b}})^{\frac{1}{b-a}}

\frac{1}{e}.(\frac{a^{b}}{b^{a}})^{\frac{a}{b-a}}

e.(\frac{b^{a}}{a^{b}})^{\frac{1}{b-a}}

\frac{1}{e}.(\frac{a^{b}}{b^{a}})^{\frac{ab}{b-a}}

None

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