Expert answers to "Solve the definite/improper integral, tell if it converges..."

embaseclielenzn

Answered question

2021-12-03

Solve the definite/improper integral, tell if it converges or diverges.

\int_{- 2}^{5} \frac{2 x + 4}{2 x^{2} + 21 x + 34} d x

Troy Lesure

Beginner2021-12-04Added 26 answers

Step 1
Given integral is

\int_{- 2}^{5} \frac{2 x + 4}{2 x^{2} + 21 x + 34} d x

Step 2

I = \int_{- 2}^{5} \frac{2 x + 4}{2 x^{2} + 21 x + 34} d x

\int_{- 2}^{5} \frac{2 x + 4}{2 x^{2} + 21 x + 34} d x + \int_{- 2}^{5} \frac{4}{2 x^{2} + 21 x + 34} d x

Using calculator we find left side integral as

2 \int_{- 2}^{5} \frac{x}{2 x^{2} + 21 x + 34} d x = {[\frac{\ln (| (x + 2) (2 x + 17) |)}{2} - \frac{21 \ln (| x + 2 |)}{26} + \frac{21 \ln (| 2 x + 17 |)}{26}]}_{- 2}^{\infty}

= - \infty

As one part is divergent so whole integral will be divergent.

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