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Question

Question: The area of the figure bounded by the curves <img src="https://cdn.pureessence.tech/canvas_416.png?t...

The area of the figure bounded by the curves and x-y-1=0 is

A

2/3

B

4/3

C

8/3

D

16/3

Answer

16/3

Explanation

Solution

Required area

=12∫−13(2y+3−y2)dy=12[y2+3y−y33]3= \frac { 1 } { 2 } \int _ { - 1 } ^ { 3 } \left( 2 y + 3 - y ^ { 2 } \right) d y = \frac { 1 } { 2 } \left[ y ^ { 2 } + 3 y - \frac { y ^ { 3 } } { 3 } \right] ^ { 3 }

=12[(9+9−9)−(1−3+13)]= \frac { 1 } { 2 } \left[ ( 9 + 9 - 9 ) - \left( 1 - 3 + \frac { 1 } { 3 } \right) \right]

=12[9+53]=163= \frac { 1 } { 2 } \left[ 9 + \frac { 5 } { 3 } \right] = \frac { 16 } { 3 }