1thnks govind and SR
2e^{-1/4}<\int_{0}^{2}{e^{x^{2}-x}}dx<2e^{2}.PROVE THE INEQUALITY.
this one is definitely a mind freak.
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3 Answers
29see the function f(x) = x2 - x..
f(x) is increasing for x > 1/2 and decreasing for x < 1/2..
so in the interval (0,2) ..f(x) will be maximum at x = 2 and minimum at x = 1/2..
put the value x = 1/2 and x = 2 in f(x) and u will get
e-1/4 < ef(x) < e2
now integrate with respect to x and put the limits..u will get the required equation
1e^{( x^2 - x ) }
iska global minimun or global maximium find karo