question_answer

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]

A) 15/2                             

B) 17/4 

C) 21/2                 

D)   15/4

Correct Answer: A

Solution :

The shaded region represents the required area in the figure. Required area \[=\int\limits_{0}^{3}{[({{x}^{2}}+2)-(x+1)]dx=\int\limits_{0}^{3}{({{x}^{2}}-x+1)}dx}\] \[=\left[ \frac{{{x}^{3}}}{3}-\frac{{{x}^{2}}}{2}+x \right]_{0}^{3}=9-\frac{9}{2}+3=\frac{15}{2}sq.\]units