pls let me know how to do this

6. Find the area of the lateral surface over the curve C in the xy-plane and under the surface z = f(x, y), where Lateral surface area = Jf(x, y)ds. f(x, y) = 2, C: line from (0, 0) to (4, 5). 7. For the vector field F(x, y) = Ax y i + 8x y'j, find the value of A for which the field is conservative. 8. Find the value of the line integral F . dr where F(x, y) = ed(zi + xzj + xk) and r(t) = 5costi + 5sintj + 6k, Outs n. (Hint: If F is conservative, the integration may be easier on an alternate path.)ON OM JA for the 9. Verify Green's Theorem by evaluating both integrals 16y dx + 16x- dy = J dy path C defined as the boundary of the region lying between the graphs of y = x and y = x. 10. Use Green's Theorem to evaluate the integral [( x2 - y )dx + 6xydy for the path C: x2 + y2 = 9