### Definite Integral

Integrated from 0 to 4 : 3x^2 dx

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Integrated from 0 to 4 : 3x^2 dx

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Consider the attached differential equation where I = (a,b) and p,q are continuous functions on I. (a) Prove that if y1 and y2 both have a maximum at the same point in I, then they can not be a fundamental set of solutions for the attached equation. (b) Let I = {see attachment}. Is {cos t, cos 2t} a fundamental set of solu

Thank you in advance for your help in solving this problem. See attached problem statement.

Derive the composite midpoint method and composite error.

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See attached file

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Problem: Given the power series for the following function (1+x)^k (a) Write the power series for (1+x)^(1/3) (b) Use the power series from part (a) to find the power series for x^3 (c) Using this series approximate the following integral (1+x^3) ^(1/3) using the first three terms

(a) Use the integral definition of the Laplace transform to compute (FUNCTION1) (b) A function g(t) has the transform (FUNCTION2). Use transform properties to compute the following. Express each in simplest form: i) (FUNCTION3) ii) (FUNCTION4) (See attachment for full question).

Find the explicit solution to the ODE 2yy'=(1+y^2) subject to y(0)=4. What is the solution if y(0)=-4? *(Please see attachment for proper citation of symbols and numbers)

Consider the vector field F=((x^2)*y+(y^3)/3)i,(i is the horizontal unit vector) and let C be the portion of the graph y=f(x) running from (x1,f(x1)) to (x2,f(x2)) (assume that x1<x2, and f takes positive values). Show that the line integral "integral(F.dr)" is equal to the polar moment of inertia of the region R lying below

Using the coordinate change u=xy, v=y/x, set up an iterated integral for the polar moment of inertia of the region bounded by the hyperbola xy=1 , the x-axis, and the two lines x=1 and x=2. Choose the order of integration which make the limits simplest THIS MESSAGE IS ADDRESSED TO ANY TA: I found something , I just want you

See attached explanation

Please assist me with the attached problems relating to functions and integrals - thank you!

Prim is primitive! In genral the moment of inertia around an axis( a line) L is: Isubl=double prim (dist(.,L)^2*delta*dA) The collection of lines parallel to the y axis have the form x=a .Let I=Isub(y) be the usual moment of inertia around the y axis I= double prim of x^2*delta*dA Let I(bar) be the moment of ine

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Evaluate integate (3sin2x - 2cos3x)dx a=pi/4 and b=pi/2