Posted by **Jessy152** on Wednesday, February 27, 2013 at 11:17am.

1. Find the area of the region bounded by the curves and lines y=e^x sin e^x, x=0, y=0, and the curve's first positive intersection with the x-axis.

2. The area under the curve of y=1/x from x=a to x=5 is approximately 0.916 where 1<=a<5. Using your calculator, find a.

3. Let R be the region bounded by y=6e^(-.2x) and y=√x and the lines x=1 and x=4. Find the volume when R is rotated about the x-axis.

4. Find the value(s) of b if the vertical line x=b divides the region between y=16-2x and the x and y-axis into 2 equal areas.

Please show work.

- Calculus -
**Steve**, Wednesday, February 27, 2013 at 11:46am
1. y=e^x sin e^x

Naturally, the first place where y=0 is at e^x=π, or x = ln π.

So, the area is just

∫[0,π] e^x sin e^x dx

That's just sin u du, so the value is 1 + cos(1)

2. just solve ln5 - ln a = .916

3. using shells,

v = ∫[1,4] 2πrh dx

where r = 1+x and h = y = 6e^(-.2x)-√x

Pretty easy integration

4. the region is just a triangle, so you want the area of the trapezoid on 0<x<b to equal the triangle on b<x<8

b(16+y(b))/2 = 1/2 (8-b)*y(b)

evaluate y at x=b, plug it in, and solve for b

## Answer this Question

## Related Questions

- Calculus AB: Area Between Curves - Hello! I'm having trouble understanding how I...
- Calculus - Find the area cut off by x+y=3 from xy=2. I have proceeded as under: ...
- brief calc - Calculate the total area of the region described. Do not count area...
- Calculus - Find the area of the region bounded by the line y=3x and y= x^3 + 2x^...
- calculus - How do I find the area bounded by the curve y = x^1/2 + 2, the x-axis...
- Calculus - We're learning disks, shells, and cylinders in school but we have a ...
- Calculus - We're learning disks, shells, and cylinders in school but we have a ...
- Calculus - Find the volume of the solid generated by rotating about the y axis ...
- calculus - A region is bounded in the second quadrant by the curve y = ln(1–x), ...
- calculus - Consider the curves y = x^2and y = mx, where m is some positive ...

More Related Questions