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Question: The area (in square units) bounded by the curve \(y = x ^ { 3 }\), \(y = x ^ { 2 }\) and the ordinat...

The area (in square units) bounded by the curve y=x3y = x ^ { 3 }, y=x2y = x ^ { 2 } and the ordinates x = 1, x = 2 is

A

1712\frac { 17 } { 12 }

B

1217\frac { 12 } { 17 }

C

27\frac { 2 } { 7 }

D

72\frac { 7 } { 2 }

Answer

1712\frac { 17 } { 12 }

Explanation

Solution

Required area =∫12(x3−x2)dx\int _ { 1 } ^ { 2 } \left( x ^ { 3 } - x ^ { 2 } \right) d x=

[x44−x33]12=(4−83)−(14−13)\left[ \frac { x ^ { 4 } } { 4 } - \frac { x ^ { 3 } } { 3 } \right] _ { 1 } ^ { 2 } = \left( 4 - \frac { 8 } { 3 } \right) - \left( \frac { 1 } { 4 } - \frac { 1 } { 3 } \right)= 43+112=16+112=1712\frac { 4 } { 3 } + \frac { 1 } { 12 } = \frac { 16 + 1 } { 12 } = \frac { 17 } { 12 }.