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Determine whether the integral is convergent or divergent. 1 35 ln x x dx 0 convergent divergent Incorrect: Your answer is incorrect.

User Advoot
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1 Answer

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Complete Question

The complete question is shown on the first uploaded image

Answer:

The integral is divergent

Explanation:

From the question we are told that

The equation given is


\int\limits^(\infty)_1 {35 (ln(x))/(x) } \, dx

Let
v = ln x

=>
(dv)/(dx) = (1)/(x)

=>
du = (dx)/(x)

So


\int\limits^(\infty)_1 {35 (ln(x))/(x) } \, dx = 35 \int\limits^(\infty)_1 { u} \, du

=>
\int\limits^(\infty)_1 {35 (ln(x))/(x) } \, dx = 35 [(u^2)/(2) ] | \left {\infty } } \atop {1}} \right.

=>
\int\limits^(\infty)_1 {35 (ln(x))/(x) } \, dx = (35)/(2) [(ln (x))^2] | \left {\infty } } \atop {1}} \right.

=>
\int\limits^(\infty)_1 {35 (ln(x))/(x) } \, dx = (35)/(2) [ [(ln (\infty))^2] - [(ln (1))^2] ]

=>
\int\limits^(\infty)_1 {35 (ln(x))/(x) } \, dx = (35)/(2) [ \infty - [(ln (1))^2] ]

=>
\int\limits^(\infty)_1 {35 (ln(x))/(x) } \, dx = (35)/(2) [ \infty ]

=>
\int\limits^(\infty)_1 {35 (ln(x))/(x) } \, dx = \infty

Hence given that the solution to the integral is
\infty then it mean that the integral is divergent

User Khan Sharukh
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