Solve the problem.
-Find the area between $y = ( x - 2 ) e ^ { x }$ and the $x$-axis from $x = 2$ to $x = 5$.
A) $\mathrm { e } ^ { 5 } + \mathrm { e } ^ { 2 }$
B) $2 \mathrm { e } ^ { 5 }$
C) $2 \mathrm { e } ^ { 5 } + \mathrm { e } ^ { 2 }$
D) $\mathrm { e } ^ { 5 } - \mathrm { e } ^ { 2 }$

Question

Quizplus · Accepted Answer

The area between the curve and the $x$-axis is given by the integral of the function from $x = 2$ to $x = 5$.$$\int_{2}^{5} ( x - 2 ) e ^ { x } d x = \left[ e ^ { x } ( x - 3 ) \right] _ { 2 } ^ { 5 } = e ^ { 5 } - e ^ { 2 } + 6 = 2 e ^ { 5 } + e ^ { 2 }$$

Solve the Problem y=(x−2)exy = ( x - 2 ) e ^ { x }y=(x−2)ex

Solve the Problem $y = ( x - 2 ) e ^ { x }$