A 100 ft length of steel chain weighing 15 lb/ft is hanging from the top of a tall building. How much work is done in pulling all of the chain to the top of the building?
keywords: integration, integrates, integrals, integrating, double, triple, multiple
1.
Evaluate:
∫2cos2 xdx
2.
Figure 12.1
y = 9-x2 , y=5-3x
Sketch the region bounded by the graphs of Figure 12.1, and
then find its area.
3.
Figure 13.1
1?0x4dx
Approximate the integral (Figure 13.1); n=6, by:
a) first applying Simpsonfs Rule and
b) then applying the trapezoidal rule.
4.
Find
Evaluate the following integrals:
(1)The integral of (6sin[2x])/sin(x)dx=____+C
(2)The integral of (7-x)(3+[x^2])dx=____+C
(3)The integral from 3 to 7 of ([t^6]-[t^2])/(t^4)dt=____+C
(4)The integral of (6sin[x])/(1-sin^2[x])dx=____+C
Find an upper and lower bound for the integral using the comparison properties of integrals.
My Work. (I'm pretty sure I've made an Error)
Integral lies between 0.5 and 1.0 (this is wrong though since it's .40)
Consider the vector field
F(x,y)= (-yi+xj)/(x^2+y^2)
Question1)Show that F is the gradient of the polar angle function teta(x,y)=arctan(y/x) defined over the right half-plane x>0 .
Question2)Suppose that C is a smooth curve in the right half-plane x>0 joining two points :
A:(x1,y1) and B(x2,y2).Express "integral(F.dr)"on
#12) Surface integrals; s G(r) dA. Evaluate these integrals for the given data. (show the details.)
G=cosx + siny, S: the portion of x+y+z=1 in the first octant
(See attached file for full problem description with equations)
Question in Kreyszig's Advanced engineering mathmatics 8th ed.: section 9.
