Solved: "Evaluate the integral. ∫−252x+42x2+21x+34"

Emeli Hagan

Answered question

2021-10-26

Evaluate the integral.

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

Delorenzoz

Skilled2021-10-27Added 91 answers

Step 1
The given integral is:

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

Step 2
Now,

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

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

= 2 \int_{- 2}^{5} \frac{x + 2}{(x + 2) (2 x + 17)} d x

= 2 \int_{- 2}^{5} \frac{1}{(2 x + 17)} d x

= 2 {[\frac{\ln (2 x = 17)}{2}]}_{- 2}^{5}

= \ln (27) - \ln (13)

=0.7308875
Step 3
Hence, the given integral is convergent.

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