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JEE Advanced 2009Paper 1
Exam
JEE Advanced
Year
2009
Paper
Paper 1
Subject
Mathematics
Chapter
Area Under Curves

JEE Advanced 2009 · Paper 1 · Mathematics · Area Under Curves

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

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

Options

  1. Ae−1e-1
  2. B∫1eln⁡(e+1−y)dy\int_1^e \ln (e+1-y) d y
  3. Ce−∫01exdxe-\int_0^1 e^x d x
  4. D∫1eln⁡ydy\int_1^e \ln y d y

Correct answer

B. ∫1eln⁡(e+1−y)dy\int_1^e \ln (e+1-y) d y

Step-by-step solution

Shaded area =e−=e-\left(\int_0^1 e^x d x\right)=1Also,Also,\quad \int_1^e \ln (e+1-y) d y<imgsrc="/api/proxy−image?url=https<img src="/api/proxy-image?url=https%3A%2F%2Ffirebasestorage.googleapis.com%2Fv0%2Fb%2Fquantrexacademy-app.firebasestorage.app%2Fo%2Fquestions%252Ffigs%252Fpyq%252Fjee_advanced%252FoZ4wxm1sBB6e6-hxsJA-BK35ZdmsmKWhMSod8yCCHEg.original.fullsize.png%3Falt%3Dmedia&clean=1&v=wm2" data-qx-orig-src="https://firebasestorage.googleapis.com/v0/b/quantrexacademy-app.firebasestorage.app/o/questions%2Ffigs%2Fpyq%2Fjee_advanced%2FoZ4wxm1sBB6e6-hxsJA-BK35ZdmsmKWhMSod8yCCHEg.original.fullsize.png?alt=media" data-qx-storage-src="https://firebasestorage.googleapis.com/v0/b/quantrexacademy-app.firebasestorage.app/o/questions%2Ffigs%2Fpyq%2Fjee_advanced%2FoZ4wxm1sBB6e6-hxsJA-BK35ZdmsmKWhMSod8yCCHEg.original.fullsize.png?alt=media"><br>=∫eqln⁡t(−dt) [put e+1−y=t⇒−dy=dt ] =∫1eln⁡tdt=∫1eln⁡ydy=1\begin{aligned}& =\int_e^q \ln t(-d t) \\ & \text{ [put }e+1-y=t \Rightarrow-d y=d t \text{ ] }\\ & =\int_1^e \ln t d t=\int_1^e \ln y d y=1 \end{aligned}$
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