19ans = 1
The equation \int_{0}^{x}{(t^2-8t+13)dt}=xsin(a/x) has a solution if sin(a/6) is equal to ?
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2 Answers
1yes answer is 1.
integrating x3-12x2+39x=3xsin(a/x)
r.h.s is always positive
hence minimum value of r.h.s is 3 while max value of l.h.s is 3
thus sin(a/x)=1 is the only solution and it occurs at x=6 put in r.h.s and verify.
remember x≠0.