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What is the area under the curve f(x) ...

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

A

`1/2` sq unit

B

`1` sq unit

C

`3/2` sq unit

D

`2` sq unit

Text Solution

Verified by Experts

The correct Answer is:
B
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
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Knowledge Check

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