Evaluate the line integral where
$$ \int_C ydx + x^2dy $$
- C1 is the path of the straight line segment from the origin, (0,0) to the point (2,18)
- C2 is the path of the parabola $y=−x^2+8x+6$ from the point (2,18) to the point (5,21)
First I looked at just c1. I found that y=9x. Then I took the integral of $$ \int_0^2 (9x+9x^2)dx =42 $$
Then I looked at c2 where I took the integral $$ \int_2^5[(-x^2+8x+6) + x^2(-2x+8)]dx $$ $$ \int_2^5(-2x^3+7x^2+8x+6)dx = 58.5 $$
I added what I got from C1 and C2 to get 100.5 but this is not correct. Can someone look at my work and see where I am going wrong?