2. [0/1.07 Points] DETAILS PREVIOUS ANSWERS HARMATHAP12 12.1.005. Evaluate the integral. Check your answer by differentiating. (Use C for the constant of integration.) x15 dx x16 + C Need Help? Read it Watch It 3. [-/1.07 Points] DETAILS HARMATHAP12 12.1.007. Evaluate the integral. Check your answer by differentiating. (Use C for the constant of integration.) 6x 7 Ox Need Help? Read it 4. [-/1.07 Points] DETAILS HARMATHAP12CR 12.1.011. Evaluate the integral. Check your answer by differentiating. (Use C for the constant of integration.) J (9 - x 1/2 ) ox 5. [-/1.07 Points] DETAILS HARMATHAP12 12.1.017. Evaluate the integral. Check your answer by differentiating. (Use C for the constant of integration.) (8 + 4 V x ) dx Need Help? Read It Watch It6. [-/1.07 Points] DETAILS HARMATHAP12 12.1.021. Evaluate the integral. Check your answer by differentiating. (Use C for the constant of integration.) x10 dx Need Help? Read It Watch it 7. [-/1.07 Points] DETAILS HARMATHAP12CR 12.1.024. Evaluate the integral. Check your answer by differentiating. (Use C for the constant of integration.) 6 dx 3VX3 Need Help? Watch It 8. [-/1.07 Points] DETAILS HARMATHAP12 12.1.027. Evaluate the integral. Check your answer by differentiating. (Use C for the constant of integration.) Need Help? Read It 9. [-/1.07 Points] DETAILS HARMATHAP12CR 12.1.031.EP. Consider the following. x + 3 dx x 3 Use algebra to rewrite the integrand. 0 / ( x 2 - 3 x 3 ) dx O ( x - 2 + 3 x - 39. [-/1.07 Points] DETAILS HARMATHAP12CR 12.1.031.EP. Consider the following. x+ 3 - dx x 3 Use algebra to rewrite the integrand. 0 / ( x 2 - 3x 3 ) dx 0 / ( x - 2 + 3 x - 3 , dx 0 / ( * 1 /3 + 3 x - 3 ) dx 0 / ( X 1 /3 - 3x 3 ) dx Integrate and simplify. (Use C for the constant of integration.) 10. [-/1.07 Points] DETAILS HARMATHAP12CR 12.1.041.MI.SA. This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to col Tutorial Exercise If the marginal revenue (in dollars per unit) for a month for a commodity is MR = -0.4x + 44, find the total revenue function. Step 1 Since the marginal revenue is found by taking the derivative of the revenue function, we can find the revenue function by taking the integral of the marginal revenue. R ( x ) - MR dx ( - 0.4x + 44 ) dx We can use the Powers of x Formula, x" dx = xn+ 1 n+ 1 + C (n * -1), for each term. Alternatively for the constant term, we can use the rule that / 1 dx = x + C. ( - 0.4x + 44 ) dx = Submit Skip (you cannot come back)11. [-/1.07 Points] DETAILS HARMATHAP12CR 12.1.041.MI. If the marginal revenue (in dollars per unit) for a month for a commodity is MR = -0.2x + 29, find the total revenue function. R (X ) = Need Help? Master It 12. [0/1.07 Points] DETAILS PREVIOUS ANSWERS HARMATHAP12 12.1.047. A factory is dumping pollutants into a river at a rate given by dx/dt = 3/4/500 tons per week, where t is the time in weeks since the dumping began and x is the number of tons of pollutants. (a) Find the equation for total tons of pollutants dumped. x (t ) = (b) How many tons were dumped during the first year? (Round your answer to two decimal places.) 1.6 x tons Need Help? Read It 13. [-/1.07 Points] DETAILS HARMATHAP12 12.1.048.MI.SA. This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the ski The rate of growth of the population of a city is predicted to be the following, where p is the population at time t is measured in years from the present. UP = 1000t1.04 dt Suppose that the current population is 100,000. Exercise (a) What is the predicted rate of growth 6 years from the present? Step 1 We are given the rate of growth formula. To find the rate of growth 6 years from the present we substitute 6 for t. This gives dp = 1000( at It == )1.04 . Submit Skip (you cannot come back) Exercise (b) What is the predicted population 6 years from the present?Click here to begin! Exercise (b) What is the predicted population 6 years from the present? Step 1 We first need to find the population as a function of t. We are given the rate of growth, or rate of change of the population with the respect to time. In other words, we are given the derivative of the population function. Thus, we can integrate the population growth function to find the population function. We have a function that is a power of t that is not equal to -1. Therefore, use the Powers of x (or t) Formula. in de = th + 1 n + 1 Therefore, p (t ) = 1000t1.04 dt 1000 + c. Submit Skip (you cannot come back) Need Help? Read It 14. [-/1.09 Points] DETAILS HARMATHAP12 12.1.048.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER The rate of growth of the population of a city is predicted to be the following, where p is the population at time t is measured in years from the present. up = 1000t1.05 dt Suppose that the current population is 100,000. (a) What is the predicted rate of growth 7 years from the present? (Round your answer to the nearest integer.) people per year (b) What is the predicted population 7 years from the present? (Round your answer to the nearest integer.) Need Help? Read it Master it Submit Assignment Save Assignment Progress