1is p=4 in the 3rd q??
1)Find the number of solutions of the equation 
here [.] is greatest integer function
2) evaluate - \int_{0}^{1}{(1+e^{-x^2}})dx
3) \textup{if }I_n=\int_{0}^{1}e^x(x-1)^n \textup{dx} \textup{ and } I_p=24e-65 \\\textup{find p}
Help in these plz.
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12 Answers
1for q no. 3 express In in a reduction form and solve... it will be something like
In=(-1)n-nIn-1.... check for urself...
1use by parts where u integrate the ex and differentiate (x-1)n
1for the 2nd... ∫(1+e-x2) dx = ∫(1+1-x21!+x42!-x63!+.......∞)dx
integrating and applying the limits from x=0 to x=1,
=(2-13.1!+15.2!_17.3!+........∞)
is dis the ans???
11
Let I=∫1+e-x2
0
e-x2 is decreasing function for 0<x<1
e0<e-x2<e-1
1<e-x2<1e
2<1+e-x2<1+1e
∫2 <∫1+e-x2 <∫1+1e
2(1-0) <∫1+e-x2 < 1+1e(1-0)
2<I<1+1e
106@raja: i meant that Q1. LHS is an even integer while RHS is an odd integer.
so we have no solutions