Monaa123
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'Determine whether or not the integral of tanx dx from 0 to pi/2 is convergent. If it is convergent, give its value.' (3 marks)

I know that it 's divergent, and the limit of tanx as x tends to pi/2 doesn't exist because tan goes off to plus and minus infinity. But I'm not sure how to word it to answer the question? (If that's even answering the question).
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tombayes
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(Original post by Monaa123)
'Determine whether or not the integral of tanx dx from 0 to pi/2 is convergent. If it is convergent, give its value.' (3 marks)

I know that it 's divergent, and the limit of tanx as x tends to pi/2 doesn't exist because tan goes off to plus and minus infinity. But I'm not sure how to word it to answer the question? (If that's even answering the question).
Consider
\lim_{\alpha \rightarrow\pi/2}[\int_0^\alpha \tan(x) dx]

solve integral in terms of alpha then show that limit does not exist.
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Smaug123
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(Original post by Monaa123)
'Determine whether or not the integral of tanx dx from 0 to pi/2 is convergent. If it is convergent, give its value.' (3 marks)

I know that it 's divergent, and the limit of tanx as x tends to pi/2 doesn't exist because tan goes off to plus and minus infinity. But I'm not sure how to word it to answer the question? (If that's even answering the question).
Bear in mind that \displaystyle \int_0^1 \dfrac{1}{\sqrt{x}} \text{d}x does converge, even though the integrand is unbounded as it approaches 0.
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