The area of the region bounded by the curves y = e x , y = lo g x and lines x = 1 , x = 2 is

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​ Required Area = ∫ 1 2 ​ ( e x − lo g x ) d x = [ e x ] 1 2 ​ − ∫ 1 2 ​ 1 lo g x d x = ( e 2 − e ) − [ x lo g x − ∫ 1 2 ​ 1 d x ] = ( e 2 − e ) − [ x lo g x − x ] 1 2 ​ = ( e 2 − e ) − [( 2 lo g 2 − 2 ) − ( 1 lo g 1 − 1 )] = e 2 − e − ( 2 lo g 2 − 2 − 0 + 1 ) = e 2 − e − ( 2 lo g 2 − 1 ) = ( e 2 − e + 1 − 2 lo g 2 ) sq. units ​

Mathematics - Area Under Curves Question with Solution | TestHub

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