Question
Sketch the graph (Do this on paper. Your teacher may ask you to turn in this graph.) and find the area of the region bounded below by the graph of the function and above by the x axis from x = 0 to x = 1.
f(x) = -xe^(-x^2)
Note: People have been telling me that the two lines do not intersect but they do there has to be an answer. please help me.
Thanks
f(x) = -xe^(-x^2)
Note: People have been telling me that the two lines do not intersect but they do there has to be an answer. please help me.
Thanks
Answers
graph of your function
http://www.wolframalpha.com/input/?i=y%3D++-xe%5E%28-x%5E2%29++from+0+to+1
notice the region will be below the x-axis, so
height = 0 - (-xe^(-x^2))
= xe^(-x^2)
area = integral (xe^(-x^2)) dx from 0 to 1
= (-1/2) e^(-x^2) from 0 to 1
= (-1/2) e^-1 - (-1/2) e^0
= -1/(2e) + 1/2
= (1/2) ( 1 - 1/e) = appr .316
http://www.wolframalpha.com/input/?i=y%3D++-xe%5E%28-x%5E2%29++from+0+to+1
notice the region will be below the x-axis, so
height = 0 - (-xe^(-x^2))
= xe^(-x^2)
area = integral (xe^(-x^2)) dx from 0 to 1
= (-1/2) e^(-x^2) from 0 to 1
= (-1/2) e^-1 - (-1/2) e^0
= -1/(2e) + 1/2
= (1/2) ( 1 - 1/e) = appr .316
Thanks for your help and for the steps. It helped me a lot.