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  2. Find the area of the region bounded by the curves y = x^2 + 2, y = x, x = 0 and x = 3.
# NCERT

Q : 3         Find the area of the region bounded by the curves  \small y=x^2+2,y=x,x=0 and \small x=3. 

Answers (1)
D Divya Prakash Singh

The area of the region bounded by the curves,

 \small y=x^2+2,y=x,x=0 and \small x=3 is represented by the shaded area OCBAO as

Then, Area OCBAO will be = Area of ODBAO - Area of ODCO

which is equal to 

\int_0^3(x^2+2)dx - \int_0^3x dx

= \left ( \frac{x^3}{3}+2x \right )_0^3 -\left ( \frac{x^3}{2} \right )_0^3

= \left [ 9+6 \right ] - \left [ \frac{9}{2} \right ] = 15-\frac{9}{2} = \frac{21}{2}units.


 

 

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