Calculus

I am doing the AP calculus review, these are the questions I have no Idea on how to do:

1. if 0<= k <=pi/2 and the area under the curve y-cosx from x=k to x=pi/2 is 0.2, then k=

2. let F(x) be an antiderivative of (ln x)^4/x If F(1)=0, then F(9)=

3. What is the equation of the line tangent to the graph of f(x)=x^4+3x^2 at the point where f'(x)=1?

4. the base of a solid is a region in the first quadrant bounded by the x-axis, the y-axis, and the line x+2y=8, as shown abobe ( a graph of right triangle with these point (0,0), (0,4), (8,0) in the first quadrant ). If cross sections of the solid perpendicular to the x-axis are semicircles, what is volume of the solid?

Table
x 2 5 7 8
f(x) 10 30 40 10

5. The function f is continuous on the closed interval [2, 8] and has values that are given in the table above. Using the subintervals [2,5], [5,7], [7,8], what is the trapezoidal approximation of integral of f(x) dx from x=2 to x=8 ?

4.134.041

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  1. limx>3

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