Cram University
 
Username: Password:

Sign up (it's free!)   | |   forgot password?

 

Calc 1 5.2

 

<== Calculus 1
Number Question Answer
See the work
1. Consider the integral

integral from 3 to 9 (4 x^2 + 4x + 5)dx
(a) Find the Riemann sum for this integral using right endpoints and n=3.
R_3 = =
(b) Find the Riemann sum for this same integral, using left endpoints and n=3.
L_3 = =
A) 1438

B) 814

The work

Point Cost: 3
2. Consider the integral

integral from 1 to 9 (3/x + 6)dx
(a) Find the Riemann sum for this integral using right endpoints and n=4.

(b) Find the Riemann sum for this same integral, using left endpoints and n=4
A) 52.72

B) 58.057

The work

Point Cost: 3
3. The following sum

(1/(1+3/n))(3/n)+(1/(1+6/n))(3/n)+...+(1/(1+3n/n))(3/n)

is a right Riemann sum for a certain definite integral
integral from 1 to b f(x)dx

using a partition of the interval [1,b] into n subintervals of equal length.

Then the upper limit of integration must be: b =
and the integrand must be the function f (x) =
b = 4

f (x) = see the work
The work

Point Cost: 3
4. Evaluate the definite integral by interpreting it in terms of areas.

integral from 2 to 7 (4x - 12) dx
30
The work

Point Cost: 3
5. Evaluate the integral below

integral from -1 to 1 sqrt(1 - x^2)dx


Do this in terms of areas. Draw a picture of the region the integral covers, and find the area using geometry.
1.571
The work

Point Cost: 2
6. Evaluate the integral below

integral from 0 to 7 abs(2 x - 6) dx


Do this in terms of areas. Draw a picture of the region the integral covers, and find the area using geometry.
25
The work

Point Cost: 2
7. Evaluate the integral by interpreting it in terms of areas:

integral from -5 to 5  (4 - abs(x))\, dx} =

15
The work

Point Cost: 3
8.
integral from 8 to 18 f(x) - integral from 8 to 17 f(x) = integral from a to b f(x)

where a = and b =
a = see the work

b = see the work

The work

Point Cost: 1
9. Let integral from 9 to 18 f(x) dx =10, integral from 9 to 12 f(x) dx=6, integral from 15 to 18 f(x)dx =8.
Find integral from 12 to 15 f(x)dx=
and integral from 15 to 12 (10 f(x)- 6)dx=
integral from 12 to 15 f(x)dx= -4

integral from 15 to 12 (10 f(x)- 6)dx= 58
The work

Point Cost: 3
10.
Given that 7 <= f(x) <= 10 for -9 <= x <= 6, use given comparison property to estimate the value of integrate from -9 to 6 f(x) dx

<= integrale from -9 to 6 f(x) dx <=
105 <= integrale from -9 to 6 f(x) dx <= 150
The work

Point Cost: 3
11. Use the Midpoint Rule to approximate the integral
integral from 10 to 17 (-1 x - 1 x^2)dx
with n=3.
-1395.6574
The work

Point Cost: 3
12. Use the Midpoint Rule to approximate
integral from -1.5 to 3.5 x^3 dx
with n=5.
35
The work

Point Cost: 3