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JEE Main 201912 JanuaryMorning Shift
Exam
JEE Main
Year
2019
Date
12 January
Shift
Morning Shift
Subject
Mathematics
Chapter
Area Under Curves

JEE Main 2019 · 12 January · Morning Shift · Mathematics · Area Under Curves

The area (in sq. units) of the region bounded by the parabola, y =...

The area (in sq. units) of the region bounded by the parabola, y=x2+2y = {x}^{2} + 2 and the lines, y=x+1,x=0y = x + 1, x = 0 and x=3x = 3, isThe area (in sq. units) of the region bounded by the parabola, y = x ^ 2 + 2 and the lines, y = x + 1, x = 0 and x = 3

Options

  1. A174\dfrac{17}{4}
  2. B212\dfrac{21}{2}
  3. C152\dfrac{15}{2}
  4. D154\dfrac{15}{4}

Correct answer

C. 152\dfrac{15}{2}

Step-by-step solution

The area (in sq. units) of the region bounded by the parabola, y = x ^ 2 + 2 and the lines, y = x + 1, x = 0 and x = 3

Area of region ABCDA=∫03[(x2+2)−(x+1)]dxABCDA = {∫}_{0}^{3}\left[\left({x}^{2} + 2\right) - \left(x + 1\right)\right]dx

=∫03(x2−x+1)dx=[x33−x22+x]03= {∫}_{0}^{3}\left({x}^{2} - x + 1\right)dx = {\left[\dfrac{{x}^{3}}{3} - \dfrac{{x}^{2}}{2} + x\right]}_{0}^{3}

=273−92+3= \dfrac{27}{3} - \dfrac{9}{2} + 3

=12−92=152= 12 - \dfrac{9}{2} = \dfrac{15}{2}

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