need help with these questions

1. Express the following limit as an integral: lim > (x) + x; sin x;) Ax from [0, ] 12- 0o i=1 2. Evaluate the following integrals using geometry and/or area formulas: A ) S $ 5 dx B) So = x+ 3 dx C) 32 V9 - x2 dx3. Evaluate the following using properties of integrals: 12 (3 x2 + 5x - 2) dx 4. Given that S6 f (x) dx = 3, S3 f (x) dx = -1, Sog(x) dx = -4, Sog(x) dx =2, find: A ) So (f ( x ) + 9 ( x ) ) dx B) So (f ( x ) - g(x) ) dx c ) S5 ( f ( x ) + g (x ) ) dx D) S (5f ( x ) - 29(x) ) dx 5. Find the net signed area between f(x) and the x-axis for S, (2 - x) dx. *(Hint: graph f) 6. Find the average value of f between a and b, and find a point c, where f (c) = fave for: f(x) = sin x, a = 0, b = 2n