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Find the area enclosed by y=e^x,x=0,y=...

Find the area enclosed by
`y=e^x,x=0,y=2,y=3`

Text Solution

Verified by Experts

Given curve is `y=e^x`
They x= In y
Area = `int_2^3xdy=int_2^3 Inycdotdy`
`[In ycdoty]_2^3-int_2^3 1/ycdotydy=[Inycdoty]_2^3-int_2^3 1/ycdotydy`
= (3 In 3 - 2 In 2) - `[y]_2^3`
`In 3^3/2^2 -(3-2)=In27/4-1`
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