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I have a small confusion in setting the limits of integration. My question is, if an integration is expressed in the following:$$\int_{1}^{b}f(x)dx$$

$1.$ Is it a necessary condition that $b>1?$

$2.$ How would the sign of the integration differ if $b<1?$

$3.$ Please refer me to some related books that address both the questions above if possible.

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1 Answer

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No, it is not necessary. The integral $$\int_1^b f(x) dx$$ is equivalent to $$-\int_b^1 f(x) dx,$$ for which now the upper limit is the greatest in the case $b<1$.

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