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JEE Advanced2009MathematicsArea Under CurvesActual

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

Options

  1. Ae-1
  2. B₁^e (e+1-y) d y
  3. Ce- ₀^1 e^x d x
  4. D₁^e y d y

Correct answer

B. ₁^e (e+1-y) d y

Step-by-step solution

Shaded area =e- ( ₀^1 e^x d x )=1 Also, ₁^e (e+1-y) d y aligned & = _e^q t(-d t) & [put e+1-y=t -d y=d t ] & = ₁^e t d t= ₁^e y d y=1 aligned

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