Question

Area bounded by the curves y = e^x, y = 2x - x² and the line x = 0, x = 1; is equal to

• A. $\frac { 3 e - 2 } { 3 }$sq. units
• B. $\frac { 4 e - 5 } { 4 }$sq. units
• C. sq. units
• D. $\frac { 3 e - 5 } { 3 }$sq. union

Answer 1

Answer: (D)

$\frac { 3 e - 5 } { 3 }$sq. union

Answer 2

For x ∈ [0, 1], 2x – x² ∈ [0, 1].

Thus e^x > 2x - x² ∀ x ∈ [0, 1].

Hence the required area

$\Delta = \int _ { 0 } ^ { 1 } \left( \left( e ^ { x } - \left( 2 x - x ^ { 2 } \right) \right) d x \right.$

$= \left( e ^ { x } - x ^ { 2 } + \frac { x ^ { 3 } } { 3 } \right) _ { 0 } ^ { 1 } = \frac { 3 e - 5 } { 5 }$ sq. units