Question

evaluate the intergral -1 to 6 (x-2)/(x^2-5x-14) dx

Answer 1

\[\int\limits_{-1}^{6} \frac{ x-2 }{ x^2-5x-14 }\]

Answer 2

\[\int\limits_{-1}^{6} {x-2 \over (x+2)(x -7)} dx\]

now do the whole partial fractions thing

Answer 3

\[\frac{ A }{ x-7 } + \frac{ B }{ x+2 }\]
then getting everything with the same denominator I get..
\[x-2 = A(x+2) + B (x-7)\]
then plugging in the different zeros, x=7 and x=-2 I solve for A and B.
\[ A = \frac{ 5 }{ 9 }\] \[ B = \frac{ 4}{ 9 }\]
Now the overall equation looks like:
\[= \frac{ 5 }{ 9 } \int\limits_{}^{} \frac{ 1 }{ x-7 } dx + \frac{ 4 }{ 9 } \int\limits_{}^{} \frac{ 1 }{ x+2 } dx\]

now what..? am I even doing this right?

Answer 4

hmm

Answer 5

yes... but in this form now its put into the ln form....