Learn more about our help with Assignments: CalculusPre-CalculusDifferential CalculusMultivariable Calculus
Search & Filtering
Calculus
using the knowledge of odd and even functions, find the Fourier series decomposition of
f(x)={2x,-π<x<π
{f(x+2π)
Calculus
Evaluate the improper integral
"\\int" ∞1 dx/(x2+4x+8)
Calculus
The surface area A of an average human body is established to be given by A(w,h)=16.54w0.75h0.25 where w is the weight and h is the height.
- Find AW(65,57) and Ah(65,57), interpret the results.
- For a 67 pounds child whose height is 57 inches determine the change in area A if weight decreases by 5 pounds and height increases by3 inches.
Calculus
Let R be the region in the first quadrant bounded by the lines y= -2x+4,y= -2x+7,y=x-2 and y=x+1.By making the substitutions u=2x+y,v=x-y and integrating over a suitable region in the u-v plane. Evaluate the integral ∫∫(2x2-xy-y2)dxdy
Calculus
- derive the reduction formulas for
- ∫cosnxdx satisfies nIn=cosn-1xsinx+(n-1)In-2
- ∫xnexdx
- ∫tannxdx
Calculus
Derive thxe reduction formulas for
- ∫(1-x5)ndx
- ∫secnxdx
Calculus
Consider the surface: S={(x,y,z)|z=sqr(x^2+y^2) and 1</=z</=3}. (a) sketch the surface S in R^3. Also show its XY-projection on your sketch. (b) evaluate the area of S, using a surface integral.
Calculus
Consider the force field F defined by F(x,y)=(6xy-12,3x^2). Use the formula(16.2) to determine the work done by the force field F in moving object in an anti clockwise direction from the point(2,0) to (-2,0) along the cycle x^2+y^2=4 by applying:(b) the fundamental theorem of line integrals
Calculus
Consider the force field F defined by F(x,y)=(6xy-12,3x^2). Use the formula(16.2) to determine the work done by the force field F in moving object in an anti clockwise direction from the point(2,0) to (-2,0) along the cycle x^2+y^2=4 by applying (a) the method for evaluating a line integral that is described in ex 16.4.1
Calculus
Let D be the region in R^3 that lies inside the cone z=sqr(x^2+y^2) above the plane z=1 and below the hemisphere z=sqr(4-x^2-y^2). (c) Express the volume of D as a triple integral using spherical coordinates. Do not evaluate the integral.
