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Mathematics · Area under the Curves

JEE Advanced 2019 — Paper 1 — Question 30

The area of the region {(x,y):xy≤8,1≤y≤x2}\left\{(x, y): x y \leq 8,1 \leq y \leq x^{2}\right\} is

  1. Option A:

    16log⁡e2−616 \log _{\mathrm{e}} 2-6

  2. Option B:

    8log⁡e2−143\quad 8 \log _{\mathrm{e}} 2-\frac{14}{3}

  3. Option C:

    16log⁡e2−14316 \log _{e} 2-\frac{14}{3}

    Correct
  4. Option D:

    8log⁡e2−738 \log _{\mathrm{e}} 2-\frac{7}{3}

Answer: C

Step-by-step solution

 Required area =∫14(8y−y)dy=(8ln⁡y−23y3/2)14=16ln⁡2−143\begin{aligned} \text { Required area } & =\int_{1}^{4}\left(\frac{8}{y}-\sqrt{y}\right) d y \\& = \left(8 \ln y-\frac{2}{3} y^{3 / 2}\right)_{1}^{4} \\& = 16 \ln 2-\frac{14}{3} \end{aligned}
Solution figure

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Exam
JEE Advanced 2019
Paper
Paper 1
Subject
Mathematics
Chapter
Area under the Curves
Topic
Area under the Curves
The area of the region \ (x, y): x y leq 8,1 leq y leq x 2 \ is | JEE Advanced 2019 PYQ with Solution · DhiX AI