Calculus Integral Calculus(I) Definite Integral as the Limit of a sum Method of Summation Definite Integral It is an explanation for finding the integral by using the method of summation(part I). Find by the method of summation the value of: (a) ∫ e^( - x)dx, where the lower limit is a and the upper limit is b
integrate: xsin (inverse)x Please help get the correct answer integrating the inverse sinx with an x in the front of it.
Complete integration by parts of x.cosx.dx
In the attached file I need to differentiate equation 9 two times so that it looks like equation 8. Please show me this step by step. (for Harmonic Motion terminology see attachment)
Integrate the following function by substituting Having trouble finding a solution when substituting x=(1-t)/(1+t). Please see attached.
1. Compute the following integrals where m and n are non-negative integers. Look out for special cases. (a) ∫ 0 --> L cos(n pi x/L)cos(m pi x/L) dx (b) ∫ 0 --> L cos(n pi x/L)sin(m pi x/L) dx Please see the attached file for the fully formatted problems.
4. Compute ∫sin^3 x cos x dx Please see the attached file for the fully formatted problem.
Heat equation with circular symmetry. Please see attached.
Find the indefinite integral and check by differentiation ∫x^3+2 dx Solve the inequality and sketch the graph of the solution on the real number line x- 5 > or = 7 Find the extreme of the function of the closed interval f(x) = 5- 2x^2, [0,3] Find dy/dx using implicit differentation for y^3 -x^2 + xy=3
Find the surface area of revolution generated by revolving the region under the curve y=2x on the interval [0,1] about the x-axis.
A. thrdrt(x^2) + 1 dx B. 4(sec^2)(x) - 5sec(x)tan(x) dx C. (e^2x)/(1+e^2) dx D. (2x + 1)^2 dx E. xe^x^2 dx F. x(1-3x^2)^4 dx G. (tan^3)(x) * (sec^3)(x) dx H. (x^2)(e^-x) dx I. (5 - x)/(2x^2 + x - 1) dx J. 1/(x^3(=) dx
Determine if the following equation is exact. If it is, solve it. If not, try to solve it by finding an integrating factor. cosx + y(sinx)y'=0
8. Heat Equation with Circular Symmetry. Assume that the temperature is circularly symmetric: u u(r,t), where r^2 x^2 | y^2. Consider any circular annulus a ≤ r ≤ b. a) Show that the total heat energy is r π f^b_a cpurdr. b) Show that the flow of heat energy per unit time out of the annulus at r b is: (see attachment
6. Let g be a primitive root of m. An index of a number a to the base (written ing a) is a number + such that g+≡a(mod m). Given that g is a primitive root modulo m, prove the following... 7. Construct a table of indices of all integers from.... 8. Solve the congruence 9x≡11(mod 17) using the table in 7. 9.
∫arctan x/[(x^2)+1] dx. See the attached file for the problem.
∫2x/(x^2 + 1) dx.
Find the area of the region 1.) y=x- x^2 points (0,1/4) (1,0) 2.) y=1/x^2 points ((1,1) (2, 1/2) Find and evaluate the integral 1.) integral 1 to 0 2xdx 2.) integral 0 to -1 (2x +1)dx 3.) integral 1 to -1 (2t -1)^2 dt 4.) integral 5 to 2 (-3x +4) dx 5.) integral 4 to 0 1/sq rt 2x +1 dx 6.) integral 2
1.) You are shown a family of graphs each of which is a general solution of the given differential equation. Find the equation of the particular solution that passes though the indicated point. dy/dx=-5x-2 point (0,2) 2.) Find the cost function for the marginal cost and fixed cost marginal costs fixe
1. Solution. Consider the integral By the Integral Test, we know that converges. Why do we choose 2 NOT 1? Since when we choose 1, then ln1=0. So, 2. Solution. Since , we have We know that diverges. So, by comparison t
See the attached file. Given that the general solution to the wave equation in one space dimension is given by where f, g are arbitrary twice continuously differentiable functions deduce that the solution s satisfying the initial conditions and for some function v, is (this is a special case of the so called
Evaluate ∫∫S √(1 + x^2 + y^2) dS where S is the helicoid: r(u,v) = u cos(v)i + u sin(v) j + vk , with 0 ≤ u ≤ 3, 0 ≤ v ≤ 2pi. Please see the attached file for the fully formatted problem.
Suppose is a radial force field,... is a sphere of radius...centered at the origin, and the flux integral.... Let be a sphere of radius... centered at the origin, and consider the flux integral... . (A) If the magnitude of... is inversely proportional to the square of the distance from the origin,what is the value of..
Evaluate the integers. Please see attached.
Find the area of the surface generated when the arc of the curve... between t=0 and y=1 is revolved about: a) the y-axis b) the x-axis c) the line y= -1 Please see attached for all twelve questions (circled problems).
Find the volume of the solid obtained by rotating the region bounded by the given curve about the specific line. (a) y=e^{5x}, y=0, x=0, x=1, about x -axis (b) x=5y-y^2, x=0, about y -axis"
In a certain city the temperature at t hours after 9 A.M. is approximated by the function T(t)=44+12sin(pi(t))/12). What is the average temperature of the city during the period from 9 A.M. to 9 P.M.?
Consider the region enclosed by the curves 2y=4sqrt{x}, y=5, 2y+4x=8. [Note: the y-axis is not a boundary of this region.] Decide whether to integrate with respect to x or y. What is the area of the region?
If a cup of coffee has temperature 95 degrees Celsius in a room where the temperature is 20 degrees Celsius, then according to Newton's Law of Cooling, the temperature of the coffee after t minutes is T(t)=20+75e^(-t/50). What is the average temperature of the coffee during the first half hour?
Find the numbers b such that the average value of f(x)=2+6x-3x^2 on the interval [0,b] is equal to 3.
Compute the integral from 0 ---> infinity. e^(-st)*(1/2)*t^2*e^-t+17*t*e^-tdt