Area under the curveHard

Question

Area of the region bounded by the curve y = ex and lines x = 0 and y = e is

Options

A.e - 1
B. ln (e + 1 - y) dy
C.e - exdx
D. ln ydy

Solution

       
Required Area = ln ydy
= (y ln y - y)1e = (e - e) - {-1} = 1.
Also, ln ydy = ln (e + 1 - y) dy
Further the required area = e × 1 - exdx.

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