Question

find g'(x)

g(x)= integral (-3/4 + t + cos(Pi/4 (t^2) + t)))

0<x<3

Answer #1

Evaluate the integral.
pi/2
3
sin2(t) cos(t)
i + 5 sin(t)
cos4(t) j + 4
sin(t) cos(t)
k dt
0

Find the length of the curve
1) x=2sin t+2t, y=2cos t, 0≤t≤pi
2) x=6 cos t, y=6 sin t, 0≤t≤pi
3) x=7sin t- 7t cos t, y=7cos t+ 7 t sin t, 0≤t≤pi/4

a). Find dy/dx for the following integral.
y=Integral from 0 to cosine(x) dt/√1+ t^2 ,
0<x<pi
b). Find dy/dx for tthe following integral
y=Integral from 0 to sine^-1 (x) cosine t dt

Let h be the function defined by H(x)= integral pi/4 to x
(sin^2(t))dt. Which of the following is an equation for the line
tangent to the graph of h at the point where x= pi/4.
The function is given by H(x)= integral 1.1 to x (2+ 2ln( ln(t) ) -
( ln(t) )^2)dt for (1.1 < or = x < or = 7). On what
intervals, if any, is h increasing?
What is a left Riemann sum approximation of integral...

Compute the line integral of f(x, y, z) = x 2 + y 2 −
cos(z) over the following paths:
(a) the line segment from (0, 0, 0) to (3, 4, 5)
(b) the helical path → r (t) = cos(t) i + sin(t) j + t k from
(1, 0, 0) to (1, 0, 2π)

With the parametric equation x=cos(t)+tsin(t), y=sin(t)-tcos(t)
, 0 ≤ t ≤ 2π)
Find the length of the given curve. (10 point)
2) In the circle of r = 6, the area
above the r = 3 cos (θ) line
Write the integral or integrals expressing the area of this
region by drawing. (10 point)

Calculate the double integral.
R 9x sin(x + y) dA, R = (0, pi/6) x (0,pi/3)

. Explain why integral of (g(x) sin(x) dx) is equal to (- g(x)
cos(x) + integral of (g'(x) cos(x) dx))

Evaluate double integral Z 2 0 Z 1 y/2 cos(x^2 )dx dy
(integral from 0 to 2)(integral from y/2 to 1) for cos(x^2) dx
dy

Solve the below boundary value equation
1. Ut=2uxx o<x<pi 0<t
2. u(0,t) = ux(pi,t) 0<t
3. u(x,0) = 1-2x 0<x<pi

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