f (t) = 2000. The interest rate tells us that r = 0,2 and the time period is T = 4 years, so that the future value of the money is

By the Fundamental Theorem of Calculus we obtain

The right answer is E.

Correct answer is A.

The price may be found as

Correct answer is D

The original integral becomes

The two curves intersect each other at the points x=-1, x=1 since x²=2-x² => x=-1, x=1. That is, the region is on the interval [-1,1]. Thus, the required area is 

We start from the trial solution

Substituting these results in the ODE gives

So, the general solution is given by

The correct answer is D.

We first need to determine the intersection points of the given curves. To do so, let us equate them:

The points satisfying the last equation are -2, 0, 2. Since there is an extra condition of x≥0, the points
of intersection are 0 and 2. Also, in the interval 0≤x≤2, we have 

and therefore the required area A is evaluated as

Therefore the correct answer is the C option.

We can find the total cost function C(x) by integrating the marginal cost function with respect to x.

The required area is

We need to find the antiderivative F such that

One of these functions satisfying

If we invoke the Fundamental Theorem of Calculus  

By the formula we have

that means the right answer is E.

The price can be found as

Using the integral formula for the producer surplus, we obtain:

The total revenue function can be found by integrating the marginal revenue. Therefore,

We need to calculate

The correct answer is B.

the correct answer is A.

Let

Turning back to original variable , one of the antiderivative of the function  

Therefore the definite integral

If we write p₀=5 in the demand function, we get that

Since the demand quantity cannot be negative, x=6. Thus, the consumer surplus can be found as: