need help with these questions

1. Find the average value of the function f (x) = ; over the interval [0, 6] and find c such that f(c) equals the average value of the function over [0, 6]. 2. Given So (2x2 - 1) dx = 15, find c such that f (c) equals the average value of f (x) =2x2 - 1 over [0, 3]. 3. Use the Fundamental Theorem of Calculus, Part 1, to find the derivative of g (r ) = SVx2 +4 dx. 4. Use FTC, Part 1, and the Chain Rule to find F' (x) for the following functions: A) F(x) = S cost dt B) F(x) = S cost dt5. Use the FTC, part 2, to evaluate the following definite integrals: A ) S2 x2 dx B ) 12 , ( x 2 + x - 2 ) dx C ) S ( 6 x2 - 5x + 2 ) dx D ) SAVE (t - 2 ) dt E) [2 2ws-w+3 dw F) S ( 4x - 6Vx2) dx w 2 G) / (2 sin 0 - 5 cos 0) de H ) S 12 x - 41 dx