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Which of the following integrals are improper? Why? $$\begin{array}{ll}{\text { (a) } \int_{1}^{2} \frac{1}{2 x-1} d x} & {\text { (b) } \int_{0}^{1} \frac{1}{...

Question

Which of the following integrals are improper? Why? $$\begin{array}{ll}{\text { (a) } \int_{1}^{2} \frac{1}{2 x-1} d x} & {\text { (b) } \int_{0}^{1} \frac{1}{2 x-1} d x} \\ {\text { (c) } \int_{-\infty}^{\infty} \frac{\sin x}{1+x^{2}} d x} & {\text { (d) } \int_{1}^{2} \ln (x-1) d x}\end{array}$$

Which of the following integrals are improper? Why? $$\begin{array}{ll}{\text { (a) } \int_{1}^{2} \frac{1}{2 x-1} d x} & {\text { (b) } \int_{0}^{1} \frac{1}{2 x-1} d x} \\ {\text { (c) } \int_{-\infty}^{\infty} \frac{\sin x}{1+x^{2}} d x} & {\text { (d) } \int_{1}^{2} \ln (x-1) d x}\end{array}$$



Answers

Which of the following integrals are improper? Why?
$$\begin{array}{ll}{\text { (a) } \int_{1}^{2} \frac{1}{2 x-1} d x} & {\text { (b) } \int_{0}^{1} \frac{1}{2 x-1} d x} \\ {\text { (c) } \int_{-\infty}^{\infty} \frac{\sin x}{1+x^{2}} d x} & {\text { (d) } \int_{1}^{2} \ln (x-1) d x}\end{array}$$


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