1.What is the integral from a to d equal to?

Answer: 5 - 4 + 1 = 2

2.Integrate 3e^x

Answer:

3.What is the integral from a to c equal to?

Answer: 5 - 4 = 1

4.Integrate 10

Answer:

5.What is the definite integral of a positive function f(x) from a to b calculating?

Answer: Area

6.Integrate (5 - 4x)

Answer: 5x - 2x^2 + C

7.Integrate 1/x from 1 toe

Answer:

8.Write an integral of a region bounded by f(x) = x/3, the x axis, line x=0 and line x=3.

Answer:

9.Find the area between x1 = 1 and x2 = 4 if y is between 0 and 3

Draw the two vertical lines x1 = 1 and x2 = 4 and two horizontal lines y=0 and y=3. You will get a square. The area of that square is 3*3 = 9

Answer: 9

10.Find the area between graph y=3x^2 and the horizontal axis for x between 1 and 2

Answer:

11.Find P(n) such that P'(n) = 3x + 4x and P(2) = 20

Integrate P'(n) and get P(n)=x^3 + 2x^2 + C

We knowP(2) is 20. Plug 2 in P(n) and solve for C:

2^3 + 2*2^2 + C = 20

C=4

Answer: P(n) = x^3 + 2x^2 + 4

12.Find the area between w(x) =3x +12and z(x) = x -3x +12if 0 x 6.

Answer:

13.Suppose MR(q) is the marginal revenue when selling q number of items. Thentheintegral of MR(q) from 0 to 50 represents the total revenue from the sale of50items.True or False?

Answer: True

14.Suppose the demand for a productis given by p=d(q) = -0.5q + 140 and the supply for the same product is given by p=s(q) =3q. For both functions, q is the quantity and p is the price in dollars.

a.Find the equilibrium point

b.Find the consumer surplus at the equilibrium price.

c.Find the producer surplus at the equilibrium price.

Answer a:Solve -0.5q + 140 =3q. The q =40. Whenqis40, we get thatp= 120. Equilibrium point(40, 120)

Answer b:solve the following expression

Answer C:solve the following expression