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

Question

Area of the region bounded by the curve y = ex and lines x = 0 and y = e is (A) e - 1 (B)  ∫ limits1e ln(e + 1 - y) dy (C)  e - ∫ limits01 ex dx  (D)  ∫ limits1e ln y dy

Tardigrade Admin · Accepted Answer

Shaded area = e - (∫ limits01 ex dx ) = 1 Also, ∫ limits1e ln (e + 1 - y) dy [put e+ 1 - y = t ⇒ - dy = dt] =∫ limitse1 ln t (-dt) = ∫ limits1e ln t dt = ∫ limits1e ln y dy = 1

Q. Area of the region bounded by the curve $y = e^{x}$ and lines
$x = 0$ and $y = e$ is

$e - 1$

$1 \int e l n (e + 1 - y) d y$

$e - 0 \int 1 e^{x} d x$

$1 \int e l n y d y$

Shaded area $= e - (0 \int 1 e^{x} d x) = 1$
Also, $1 \int e l n (e + 1 - y) d y [p u t e + 1 - y = t \Rightarrow - d y = d t]$
$= e \int 1 l n t (- d t)$ $= 1 \int e l n t d t$ $= 1 \int e l n y d y = 1$

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

e−1

1∫e​ln(e+1−y)dy

e−0∫1​exdx

1∫e​lnydy