Question

Evaluate the following integral:

1. *∫xse**c(square)**xdx*

*2.*
*∫**e(power)**t{root(**1+**e(power)**2t)}**dt*

Answer #1

1. Evaluate ∫tan^2 xsec^4 xdx
2. Evaluate the indefinite integral
∫sin^6 tcos^3 tdt=

1. Evaluate ???(triple integral) E
x + y dV
where E is the solid in the first octant that lies under the
paraboloid z−1+x2+y2 =0.
2.Evaluate ???(triple integral) square root ?x^2+y^2+z^2 dV
where E lies above the cone z = square root x^2+y^2 and between
the spheres x^2+y^2+z^2=1 and x^2+y^2+z^2=9

(1) Show that -infinity to infinity ∫ xdx is divergent.
(2) Show that lim t→∞ definite integral -t to t ∫ xdx = 0. This
shows that we cannot define ∫ ∞ −∞ xdx= lim t→∞ definite integral-1
to t ∫ xdx

Evaluate the integral. (sec2(t) i + t(t2 + 1)7 j + t3 ln(t) k)
dt

Find the general solution of the equation.
d^2y/dt^2-2t/(1+t^2)*dy/dt+{2/(1+t^2)}*y=1+t^2

A space curve C is parametrically parametrically defined by
x(t)=e^t^(2) −10,
y(t)=2t^(3/2) +10,
z(t)=−π,
t∈[0,+∞).
(a) What is the vector representation r⃗(t) for C ?
(b) Is C a smooth curve? Justify your answer.
(c) Find a unit tangent vector to C .
(d) Let the vector-valued function v⃗ be defined by
v⃗(t)=dr⃗(t)/dt
Evaluate the following indefinite integral
∫(v⃗(t)×i^)dt. (cross product)

P(W < t) = 1/12(t^2+ 2t^3) for 0 ≤ t ≤ 2. Write an integral
for E[√(W+ 3) ].

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

Find the length of the curve.
(square root 2) t i + et j + e−t k
0 ≤ t ≤ 6

For problem 1 to 3, use r(t)= <e^2t cost, e^2t sint, e^2t>
to find each of the following at t = 0.
1, T(t)
2, N(t)
3, Curvature

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 11 minutes ago

asked 14 minutes ago

asked 28 minutes ago

asked 28 minutes ago

asked 28 minutes ago

asked 29 minutes ago

asked 29 minutes ago

asked 34 minutes ago

asked 48 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago