Please help with the following questions:
1. Use the limit process to find the area of the region between the graph of the function and the axis over the given interval. Sketch the region.
y = 4 - x^2, [-2,2]
2. Find the area of the regionbounded by the graphs of the equations.
y = x^3 + x, x = 2, y = 0

Please help me find solutions to these problems. Please show your work along with explanations.
Thank you for your help!
1. Find the area of the regionbounded by the graph of , the -axis, and the line .
2. Find the derivative: .
13. Find

1. Solve the following differential equation:
-2yy' +3x^2 SQRT(4-y^2) =5x^2 SQRT(4-y^2) , -2 < y < +2
2. Let f(x) = ax^2 , a>0 , and g(x) = x^3
Find the value of a which yields an area of PI (i.e. 3.14159) for regionbounded by figure, y-axis and line x=1.

A)The regionbounded by y = e^2x, y = e^x, x = 0, and x = 2 is rotated around the x-axis. Find the volume.
b)Consider the regionbounded by y = x^2, y = 3, and the y-axis. Find the volume of the solid obtained by rotating the region around the y-axis.

Please help with the following problem. Provide step by step calculations for each.
The average value of f(x) = 1/x on the interval [4, 16] is
(ln 2)/3
(ln 2)/6
(ln 2)/12
3/2
0
1
none of these
Find the area, in square units, of the region b

Question (1)
What is the volume of the solid of revolution obtained by rotating the regionbounded by y = 1 and y = 5 - x^2 around the X-axis.
Question (2)
Find the volume of the solid of revolution obtained by rotating the regionbounded by y = 1 and y = Tan x about the x-axis from x = 0 to x = pi/4.
See attached file

1. Determine the value of f(x)=-5x^3+7x on [-1,2].
2. Determine the area of region bound by f(x)=-2x^2+x+6 and the x-axis on [0,3].
3. Determine the area of the regionbounded by f(x)=x^2 - 4 and g(x)=x+2
4. Determine the area of the regionbounded by f(x)=x+6 and g(x)=-x^2+2 on the interval on [-2, 2].
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