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estro

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Hello,

I have question about using Dirichlet's Convergence Test which states:

1. if f(x) is monotonic decreasing and [tex]\lim_{x\rightarrow \infty} f(x)=0[/tex]

2. [tex]G(x)=\int_a^x g(t)dt[/tex] is bounded.

Then [tex]\int_a^\infty f(x)g(x)dx[/tex] is convergent.

But what about the following situation:

f(x)=1/x

g(x)=cosxsinx

Can I say that [tex]\int_a^x costsintdt=\int_{sina}^{sinx} tdt=t^2/2=sin^2x/2-sin^2a/2[/tex]

for every x G(x) is bounded and by the Dirichlet's Convergence Test the integral is convergent?

I have question about using Dirichlet's Convergence Test which states:

1. if f(x) is monotonic decreasing and [tex]\lim_{x\rightarrow \infty} f(x)=0[/tex]

2. [tex]G(x)=\int_a^x g(t)dt[/tex] is bounded.

Then [tex]\int_a^\infty f(x)g(x)dx[/tex] is convergent.

But what about the following situation:

f(x)=1/x

g(x)=cosxsinx

Can I say that [tex]\int_a^x costsintdt=\int_{sina}^{sinx} tdt=t^2/2=sin^2x/2-sin^2a/2[/tex]

for every x G(x) is bounded and by the Dirichlet's Convergence Test the integral is convergent?

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