Multiplex! for JEE

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 \(b>a\).

0 \[\frac{1}{e}.(\frac{b^{b}}{a^{a}})^{\frac{1}{b-a}}\] \[\frac{1}{e}.(\frac{a^{a}}{b^{b}})^{\frac{1}{b-a}}\] \[\frac{1}{e}.(\frac{a^{b}}{b^{a}})^{\frac{a}{b-a}}\] \[e.(\frac{b^{a}}{a^{b}})^{\frac{1}{b-a}}\] \[\frac{1}{e}.(\frac{a^{b}}{b^{a}})^{\frac{ab}{b-a}}\] None