JEE Mains · Maths · STD 12 - 8. Application and integration
The area enclosed by the curves \(y=\log _{ t }\left( x + e ^{2}\right)\), \(x=\log _{ e }\left(\frac{2}{ y }\right)\) and \(x =\log _{ e } 2\), above the line \(y =1\) is.
- A \(2+e-\log _{e} 2\)
- B \(1+e-\log _{e} 2\)
- C \(e -\log _{ e } 2\)
- D \(1+\log _{ e } 2\)
Answer & Solution
Correct Answer
(B) \(1+e-\log _{e} 2\)
Step-by-step Solution
Detailed explanation
Required area is \(=\int_{0-0^{2}}^{0} \ln \left( x + e ^{2}\right)-1 dx +\int_{0}^{\ln 2} 2 e ^{- x }-1 dx =1+ e -\operatorname{\ell n} 2\)
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