Question 12.20: Evaluate the definite integral ∫ 5^6 (6x^0.5 − 3x^−2 + 85x^4......

Basic Mathematics for Economists [1185418]

Evaluate the definite integral

$\int_{5}^{6}{(6x^{0.5} − 3x^{−2} + 85x^4)dx}$

Step-by-Step

The 'Blue Check Mark' means that this solution was answered by an expert.
Learn more on how do we answer questions.

$\int_{5}^{6}{(6x^{0.5} − 3x^{−2} + 85x^4)dx}$ = $\left[4x^{1.5} + 3x^{−1} + 17x^5\right]_5^6$
             = (58.787752 + 0.5 + 132,192) − (44.72136 + 0.6 + 53,125)
             = 132,251.29 − 53,170.32
             = 79,080.97

Related Answered Questions

Question: 12.13

At what level of K is the function Q = 12K^0.4(160 − 8K)^0.4 at a maximum? (This is Example 11.1 (reworked) which was not completed in the last chapter.) ...

Verified Answer:

The objective is to find the value of K which maxi...

Question: 12.14

In the theory of individual labour supply it is assumed that an individual derives utility from both leisure (L) and income (I ). Income is determined by hours of work (H ) multiplied by the hourly wage rate (w), i.e. I = wH . Assume that each day a total of 12 hours is available for an individual ...

Verified Answer:

Given a maximum working day of 12 hours, then hour...

Question: 12.21

For the non-linear demand function p = 1,800 − 0.6q² and the corresponding marginal revenue function MR = 1,800 − 1.8q² , use definite integrals to find: (i) TR when q is 10; (ii) the change in TR when q increases from 10 to 20; (iii) consumer surplus when q is 10 ...

Verified Answer:

(i) TR when q is 10 will be

\int_{0}^{10} ...

Question: 12.19

If a firm faces the marginal cost schedule MC = 180 + 0.3q² and the marginal revenue schedule MR = 540 − 0.6q² and total fixed costs are £65, what is the maximum profit it can make? (Assume that the second-order condition for a maximum is met.) ...

Verified Answer:

Profit is maximized when MC = MR. Therefore, 180 +...

Question: 12.18

What total revenue will a firm earn if it charges a price of £715 and its marginal revenue function is MR = 960 − 0.15q² ? ...

Verified Answer:

As we have established that the integral of this f...

Question: 12.16

If a firm spends £650 on fixed costs what is its total cost function if its marginal cost function is MC = 82 − 16q + 1.8q² ? ...

Verified Answer:

We know that for any cost function

\int [/...

Question: 12.17

If MR = 520 − 3q^0.5 what is the corresponding TR function? ...

Verified Answer:

TR =

\int

MR dq =

\int [/...

Question: 12.2

If y = (48 + 20x^−1 + 4x + 0.3x²)^4 , what is dy/dx? ...

Verified Answer:

Let z = 48 + 20

x^{-1}

+ 4x + 0.3x² ...

Question: 12.1

The present value of a payment of £1 due in 8 years’ time is given by the formula PV = 1 /(1 + i)^8 where i is the given interest rate. What is the rate of change of PV with respect to i? ...

Verified Answer:

If we let z = 1 + i (1) then we can w...

Question: 12.15

Find the following integrals: (i) ∫ 30x^4 dx (ii) ∫(24 + 7.2x)dx (iii) ∫ 0.5x^−0.5 dx (iv) ∫(48x − 0.4x^−1.4)dx (v) ∫(65 + 1.5x^−2.5 + 1.5x²)dx ...

Verified Answer:

(i) y = 6

x^{5}

+ C(ii) y = 24x + 3....