What is the area under the curve `f(x) = xe^(x)` above the x -axis and between thelines `x = 0` and `x = 1` ?

Options

A. `1/2` sq unit
B. `1` sq unit
C. `3/2` sq unit
D. `2` sq unit

Answer

B

Explanation

Given curve is `f(x) =xe^(x), x = 0`and `x = 1`.
So, Required Area = `int_(0)^(1)f(x) dx = int_(0)^(1) xe^(x) dx`
Let x be the first function and `e^(x)` be the second function then by parts
`= [xe^(x) - inte^(x) dx]_(0)^(1) = [xe^(x) -e^(x)]_(0)^(1)`
` = (e-e) - (0-1) = 1` sq units