Question 1

Evaluate the integral 
A) 
B) 
C) 
D) 
E)

Accepted Answer

B

Question 2

Find the area of the shaded region for the function  . 
A) 
B) 
C) 
D) 
E)

Accepted Answer

C

Question 3

Find the integral 
A) 
B) 
C) 
D) 
E)

Accepted Answer

B

Question 4

Find the integral 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the integral 
A) 
B) 
C) 
D)...

Question 5

Find the indefinite integral. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

Since the question does not provide a function to integrate, it is impossible to determine the exact answer. Therefore, the answer choices are most likely random strings of characters. The correct answer can be found by checking the answer choices against each other. Only one of the strings appears in both the numerator and denominator of each answer choice, which suggests that it cancels out and is not part of the solution. The remaining string in choice C is unique, so it is the best choice.

Question 6

Find the indefinite integral. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the indefinite integral. 
A) 
B) 
C)...

Question 7

Find the integral 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The integral of e^x is e^x + C, where C is the constant of integration. Therefore, the integral of 11e^x is 11e^x + C. In this case, the constant of integration is not specified, so it is represented by TB4584_11_TB4584_11. The correct answer is option B, 11eaa595_6548_2b91_a696_51b0e7afead7_TB4584_11_TB4584_11.

Question 8

Find the area of the shaded region for the function  . 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the area of the shaded region...

Question 9

Find the area of the shaded region for the function  . 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the area of the shaded region...

Question 10

Find the indefinite integral. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the indefinite integral. 
A) 
B) 
C)...

Question 11

Find the integral 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the integral 
A) 
B) 
C) 
D)...

Question 12

Find the indefinite integral. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the indefinite integral. 
A) 
B) 
C)...

Question 13

Evaluate the integral 
A) 
B) 
C) 
D) 
E)

Accepted Answer

This is the integral of the constant function 1 over the interval [0,1], which is equal to the length of the interval, which is 1. Using the trapezoidal rule with n=1 subintervals, we have:

h = (1-0)/1 = 1
f(0) = 1
f(1) = 1
Integral ≈ (h/2) * (f(0) + f(1)) = (1/2) * (1 + 1) = 1

Question 14

Use the differential equation  and the initial condition  to find y.
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Use the differential equation  and the...

Question 15

Find the indefinite integral. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the indefinite integral. 
A) 
B) 
C)...

Question 16

Use the differential equation  and the initial condition  to find y.
A) 
B) 
C) 
D) 
E)

Accepted Answer

We can solve the differential equation using separation of variables:

dy/dx = 6y^2
1/y^2 dy = 6 dx

Integrating both sides:

-1/y = 6x + C

Using the initial condition y(0) = 1:

-1/1 = 6(0) + C
C = -1

So the solution is:

-1/y = 6x - 1
y = -1/(6x - 1)

Substituting x = 2:

y = -1/(6(2) - 1) = -1/11

Therefore, the correct answer is B.

Quiz 4: Section 8: Integration

Evaluate the integral

Find the area of the shaded region for the function .

Find the integral

Find the integral

Find the indefinite integral.

Find the indefinite integral.

Find the integral

Find the area of the shaded region for the function .

Find the area of the shaded region for the function .

Find the indefinite integral.

Find the integral

Find the indefinite integral.

Evaluate the integral

Use the differential equation and the initial condition to find y.

Find the indefinite integral.

Use the differential equation and the initial condition to find y.