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Determine the (a) consumers surplus and (b) producers surplus for the given demand and supply curves..$$p=\sqrt{x+14}, p=\sqrt{36-x}$$

(a) $17 / 3$(b) 6.59

Calculus 1 / AB

Chapter 5

Integration and its Applications

Section 8

Applications of the Definite Integral

Integrals

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Lectures

05:53

In mathematics, an indefinite integral is an integral whose integrand is not known in terms of elementary functions. An indefinite integral is usually encountered when integrating functions that are not elementary functions themselves.

40:35

In mathematics, integration is one of the two main operations of calculus, with its inverse operation, differentiation, being the other. Given a function of a real variable (often called "the integrand"), an antiderivative is a function whose derivative is the given function. The area under a real-valued function of a real variable is the integral of the function, provided it is defined on a closed interval around a given point. It is a basic result of calculus that an antiderivative always exists, and is equal to the original function evaluated at the upper limit of integration.

03:17

Find the consumers' s…

05:11

Consumer Surplus and Produ…

05:13

05:41

now hear this problem where to find the consumer's surplus for the given demand cove. Which is P is equal to underwrote 16 -0.02 times six At the given sales level which is X. is the goals to 350. Now, since 350 units are sold, so the price must be Be calls to you can put the value of X. S. years under route 16 -0.02 times 50. So we'll get this value to be three. No, the consumer's surplus would be integration 0-3 50 function. We have under look 16 0. So it's 02 weeks -3. Not be eggs. Now we can easily evaluate this integral. So it would be equals two. Now the integration of underwrote 16. -0.02 weeks will be So 16 -0.02 X. to the power one x 2 plus one, divide by one by two plus one, multiplied with -0.02 minus the integration of three is three X. And the limit we have 0-3 50 now we're gonna solve this so You can put the limit to be as 350. So let me first simplify this. So this would be 16 -0.02 X. To the sorry it's X. to the power 3/2. And here it would become too over three. and denominator is as it is zero 02 minus three X. And the limit is strong 0- 350. Now we can put the limits upper limit minus the lower limit. Now we can put the upper limit minus the lower limit. So it will be To divide by three. This is 16 -0.02 multiplied with a parliament. We have 350 to the power three over to divide by 0.0 to negative sign as it is -3 times 3 50. This is our parliament minus the lower limit. So low limited we have zero. So this would become zero. So no need to write this one and here it this would be zero. So other times we have to over three Times 16 to the Power three over to divide by -0.02. Now we can solve this by using a calculator and we'll get the answer to be nearly 183 33 Therefore the surplus, we have $1.83.33. So this is a final answer. I hope you got a problem. Thank you.

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