Evaluate using Integration by parts

[waealu]

Homework Statement

If g(1)=3, g(5)=8 and the integral from 1 to 5 of g(x)dx=-9. Then, evaluate the integral from 1 to 5 of xg'(x)dx.

2. Homework Equations and attempt at solution

I used integration by parts to get =xg(x)-(integral of)g(x)dx from 1 to 5. Then substituting in, I get ((5)(8)+9)-((1)(3)+9)=37

Apparently that answer is incorrect. What am I missing? Thanks.

 

[stevenb]

Homework Statement

If g(1)=3, g(5)=8 and the integral from 1 to 5 of g(x)dx=-9. Then, evaluate the integral from 1 to 5 of xg'(x)dx.

2. Homework Equations and attempt at solution

I used integration by parts to get =xg(x)-(integral of)g(x)dx from 1 to 5. Then substituting in, I get ((5)(8)+9)-((1)(3)+9)=37

Apparently that answer is incorrect. What am I missing? Thanks.

You didn't think of the integral in the right way. You are already provided the answer for the complete integral of g(x)dx. You don't need to apply it twice.

you should get xg(x) from 1 to 5 giving you 40-3=37. Then the integral will give you --9=+9

Final answer is 37+9=46

Note: $$\int_a^b u\; dv=[uv]_a^b-\int_a^b v\; du$$