Find the center of mass between the two functions x^2 and y^2

Find the derivative of y = integral from x^2 to x^3 sin(t^3) dt using the fundamental theorem of calculus

Find the centroid of the region bounded by the given curves sinx and cosx

Find the centroid of the region bounded by the given curves sinx and cosx o and pi:4

Find the derivative of dy:dx = sqrt(1-2y^3)

Find the cross product of a and b using a_1 a_2 a_3 ...

Find the arclength y = ln(1 - x^2), 0

Solve the differential equation x'' - x' - 2x = e^tcost -t^2 + cos^3(t)

The linear transformation T1:R2\toR2 is given by T(x,y)=(2x+3y,8x+13y)

The input is a constant multiple of an exponentila e^(at0. Suppose that there is a particular solution of the fomr Ae^at for some constant A. Find the constant A and determine the particular and general solution.

The half-life of plutonium is approximately 13 years. How much of a sample wieghing 8 g will remain after 110 years?

The differential equation is nonlinear in the form dx:dt=f(t,x), but linear (after some algebraic manipulations) if written as dt:dx=1:f(t,x). Find the general solution of the differential equation.

The current I(t) in an RLC circuit with voltage source E(t) is governed by thinitial value problem

The cone z=sqrt(x^2+y^2) and the plane z=1+y fin a vector function that represnets the curve intersection of the two surfaces

The closed interval [a,b] is a partitioned into n subintervals each of width Delta x = b-a:n if u is any number in the ith subinterval, what is lim

The amount of carbon 14 present after t years is given by the exponential equations. A sample from a refuse doposit

Evaluate the integral e^sqrt(x)

Evaluate the integral cos^3(x)sin(2x) dx from 0 to pi:2

Evaluate the integral (1 - tan(theta)):(1 + tan(theta)) dtheta

Evaluate the indefinite integral x:(x+2)^(2:3) hint let u = x+2

Evaluate the improper integral, or state that it diverges x:sqrt(1-x) from 0 to 1

Evaluate the improper integral from pi:4 to pi:2 tan (x) dx

Evaluate the improper integral, or state that it diverges

Evaluate the improper integral, or state that it diverges dx:(x^2+4)

Evaluate the improper integral, or state that it diverges dx:xln(x)

Evaluate the improper integral, or state that it diverges tan x from pi:4 to pi: 2