JEE Main 12 Jan 2019 Morning Question 2

Question: 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, $ is [JEE Main Online Paper Held On 12-Jan-2019 Morning]

Options:

A) 15/2

B) 17/4

C) 21/2

D) 15/4

Show Answer

Answer:

Correct Answer: A

Solution:

  • The shaded region represents the required area in the figure.
    Required area $ =\int\limits_0^{3}{[(x^{2}+2)-(x+1)]dx=\int\limits_0^{3}{(x^{2}-x+1)}dx} $ $ =[ \frac{x^{3}}{3}-\frac{x^{2}}{2}+x ]_0^{3}=9-\frac{9}{2}+3=\frac{15}{2}sq. $ units