A function y=f(x) satisfies the condition f′(x)sinx+f(x)cosx=1 being bounded whenx→0. Ifl=∫π/20f(x)dx, then

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A function y=f(x) satisfies the condition f′(x)sinx+f(x)cosx=1 being bounded whenx→0. Ifl=∫π/20f(x)dx, then

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[a] sinxdydx+ycosx=1 dydx+ycotx=cosecx IF =e∫cotxdx=eln(sinx)=sinx ysinx=∫cosecx.sinxdx=x+C IF x=0,y is finite ∴C=0 y=x(cosecx)=xsinx Now, l

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Question Text	A function y=f(x) satisfies the condition f′(x)sinx+f(x)cosx=1 being bounded whenx→0. Ifl=∫π/20f(x)dx, then
Answer Type	Text solution:1
Upvotes	150