Question

1. If f(x) = ∫10/x t^3 dt then: f′(x)= ? and f′(6)= ?

2. If f(x)=∫x^2/1 t^3dt t then f′(x)= ?

3. If f(x)=∫x3/−4 sqrt(t^2+2)dt then f′(x)= ?

4. Use part I of the Fundamental Theorem of Calculus to find the derivative of h(x)=∫sin(x)/−2 (cos(t^3)+t)dt. what is h′(x)= ?

5. Find the derivative of the following function:
F(x)=∫1/sqrt(x) s^2/ (1+ 5s^4) ds using the appropriate form of the
Fundamental Theorem of Calculus.

F′(x)= ?

6. Find the definitive integral: ∫8/5 (d/dt sqrt(2+3t^4)) dt

Answer #1

1. y=∫upper bound is sqrt(x) lower bound is 1,
cos(2t)/t^9 dt
using the appropriate form of the Fundamental Theorem of
Calculus.
y′ =
2. Use part I of the Fundamental Theorem of Calculus to find the
derivative of
F(x)=∫upper bound is 5 lower bound is
x, tan(t^4)dt
F′(x) =
3. If h(x)=∫upper bound is 3/x and lower
bound is 2, 9arctan t dt , then
h′(x)=
4. Consider the function f(x) = {x if x<1, 1/x if x is >_...

1. Use Part 1 of the Fundamental Theorem of Calculus to find the
derivative of the function.
2. Use Part 1 of the Fundamental Theorem of Calculus to find the
derivative of the function.
y =
4
u3
1 + u2
du
2 − 3x
3. Evaluate the integral.
4. Evaluate the integral.
5. Evaluate the integral.
6. Find the derivative of the function.

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...

1. Find the derivative of
f(x)= √4-sin(x)/3-cos(x)
2. Find the derivative of
1/(x^2-sec(8x^2-8))^2

The function f(x) = sin (5x^2 ) does not have an antiderivative
in terms of the commonly known functions.
Use the Fundamental Theorem of Calculus to find a function F(x)
satisfying F'(x) = sin (5x2 )and F(4) = 5 .

(a) Is the vector field F = <e^(−x) cos y, e^(−x) sin y>
conservative?
(b) If so, find the associated potential function φ.
(c) Evaluate Integral C F*dr, where C is the straight line path
from (0, 0) to (2π, 2π).
(d) Write the expression for the line integral as a single
integral without using the fundamental theorem of calculus.

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

(1 point) Let F(x)=∫o,x sin(6t^2) dt F(x)=∫0xsin(6t^2) dt. The
integrals go from 0 to x
Find the MacLaurin polynomial of degree 7 for F(x)F(x).
Use this polynomial to estimate the value of ∫0, .790 sin(6x^2) dx
∫0, 0.79 sin(6x^2) dx. the integral go from 0 to .790

Let F ( x , y , z ) =< e^z sin( y ) + 3x , e^x cos( z ) + 4y
, cos( x y ) + 5z >, and let S1 be the sphere x^2 + y^2 + z^2 =
4 oriented outwards Find the flux integral ∬ S1 (F) * dS. You may
with to use the Divergence Theorem.

find the derivative of the functions
T(theta)=cos(theta^2 + 3theta - 10)
f(x)=(3x/(x^2-1))^3/2

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