Question

Write out the form of the partial fraction decomposition of the function appearing in the integral:

integral [(2 x - 250)(x² + 6 x - 55)]dx
Determine the numerical values of the coefficients, A and B, where Astudent submitted image, transcription available belowB and

(2 x - 250)/(x² + 6 x - 55) = A/denominator + B/denominator

Answer 1

The partial fraction decomposition of the given integral is (A/(x-5)) + (B/(x+11)), where A = -15 and B = 17.

Step-by-step explanation:

The given integral can be rewritten as:

∫ [(2x - 250)(x² + 6x - 55)]dx

To decompose this into partial fractions, we first factorize the denominator:

x² + 6x - 55 = (x - 5)(x + 11)

Now we can write the integral as:

∫ [(A/(x-5)) + (B/(x+11))]dx

To determine the values of the coefficients A and B, we need to find a common denominator and then equate the numerators. By multiplying both sides by the common denominator, we get:

(2x - 250) = A(x + 11) + B(x - 5)

Solving for A and B, we find that A = -15 and B = 17.