## sammii2u 2 years ago evaluate the intergral -1 to 6 (x-2)/(x^2-5x-14) dx

1. sammii2u

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

2. slaaibak

$\int\limits_{-1}^{6} {x-2 \over (x+2)(x -7)} dx$ now do the whole partial fractions thing

3. sammii2u

$\frac{ A }{ x-7 } + \frac{ B }{ x+2 }$ 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?

4. Goten77

hmm

5. Goten77

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

6. Goten77

|dw:1358132021880:dw|

7. Goten77

you got it into the like ... i cant think of the name but its a form name.... but you did it right

8. sammii2u

right. so it would be $= \left[ \frac{ 5\ln |x-7| }{ 9 } + \frac{ 4\ln |x+2| }{ 9 } \right] _{-1} ^{6}$ and then I evaluate it at x=6 and then subtract x=-1 ?

9. slaaibak

yeah. nice job.