Question

b.) express the following improper integral as limits of proper integral(s). do not evaluate the integral(s).

\\( \int _ { 2 } ^ { \infty } \frac { 3 x } { 4 - x ^ { 2 } } d x \\)

Explanation:

Step1: Use the definition of improper integral

By definition, \(\int_{a}^{\infty}f(x)dx=\lim_{b
ightarrow\infty}\int_{a}^{b}f(x)dx\). Here \(a = 2\) and \(f(x)=\frac{3x}{4 - x^{2}}\), so \(\int_{2}^{\infty}\frac{3x}{4 - x^{2}}dx=\lim_{t
ightarrow\infty}\int_{2}^{t}\frac{3x}{4 - x^{2}}dx\)

Answer:

\(\int_{2}^{\infty}\frac{3x}{4 - x^{2}}dx=\lim_{t
ightarrow\infty}\int_{2}^{t}\frac{3x}{4 - x^{2}}dx\)