JEE Main & Advanced
JEE Main Paper (Held On 12-Jan-2019 Morning)
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