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Question

f(x)=1sinx(π2x)4.cosx.(8x3π3)(xπ2) f(π/2) if f(x) is continuous at x=π/2 is aπ2b. Find ba

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Solution

Putπ2x=t
Ltt01cost(2t)4.sint{(π2t)3π3}
Applying factors of a3b3
=Ltt02sin2(t/2).t16t4[2t{((π2t)2+π2+π(π2t))}] =14(t/2)2t2,{3π26πt+4t2}=3π216.
Ans: 13

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