Question Instructions

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1 11 Bsic: Clc II Intro ( ) Question Instructions Red tody's Notes nd Lerning Gols Do not use clcultor on this ssignment. When you re quizzed/tested on this mteril, you will not e le to use your clcultor.

2 1. Question Detils re dy1 x^2 [ ] Find the shded re under the curve y following these steps. 1. How tll is the rectngle? (Answer in terms of x.) in 2. How wide is the rectngle? (Use pproprite differentil.) in 3. Write the re of the rectngle s formul using x nd dx. in 2 4. Wht re the upper nd lower ounds of x for the shded re under the curve? 5. Set up the definite integrl to find the shded re under the curve. 6. Compute your integrl using the Fundmentl Theorem of Clculus to find the shded re under the curve. (Do not use clcultor!) in 2

2. Question Detils re dy1 sin [3440731] 1. Set up the definite integrl to find the shded re under the curve.

Compute your integrl using the Fundmentl Theorem of Clculus to find the shded re under the curve. (Do not use clcultor!) m 2 3.

3 2. Question Detils re dy1 sin [ ] 1. Set up the definite integrl to find the shded re under the curve. where the ounds of integrtion re 2. Compute your integrl using the Fundmentl Theorem of Clculus to find the shded re under the curve. (Do not use clcultor!) m 2 3. Question Detils volume dy1 coin [ ] In the next few questions, we will e exploring volume. We will show you how to use clculus to find volumes in more detil lter in the semester. Consider coin with rdius r nd width dx. Wht is its volume?

4 4. Question Detils volume dy1 x^2 [ ] Find the volume of this solid y following these steps. 1. Wht is the rdius of the coin in terms of x? in 2. Wht is the width of the coin? (Use pproprite differentil.) in 3. Write the volume of the coin s formul using x nd dx. in 3 4. Set up the definite integrl to find the volume of the solid. where the ounds of integrtion re 5. Compute your integrl using the Fundmentl Theorem of Clculus to find the volume of the solid. (Do not use clcultor!) in 3

5 5. Question Detils volume dy1 sin [ ] Set up the definite integrl to find the volume of the solid. where the ounds of integrtion re 6. Question Detils intro trig integrls [ ] The lst question involved n integrl of type tht you hve not yet lerned to evlute. You will lern how to evlute more integrls involving trigonometric functions lter this semester. One technique is to use trigonometric identities to simplify the prolem. For exmple: 1. Use the trig identity sin (x) = cos(2x) to find the ntiderivtive. 2 2 sin (x) dx = cos(2x) dx = + C Compute this integrl using the Fundmentl Theorem of Clculus nd the ove ntiderivtive. π sin 2 (x) dx = π 0

6 7. Question Detils dy1 intro moment [ ] In the next few questions, we will e exploring moment. We will go into moment in more detil lter in the semester. For now, think of the moment of weighted region s its tendency to rotte out the yxis. To find the moment of thin rectngle, multiply the weight of the rectngle y its distnce from the yxis. 1. Write the re of the rectngle s formul using h nd dx. in 2 l 2. Weight is the re multiplied y density. Suppose the density is 1. Find the weight of the in 2 rectngle. l 3. Wht is the distnce of the rectngle from the yxis? in 4. The moment of the rectngle out the yxis is the weight of the rectngle multiplied y its distnce from the yxis. Find the moment of the rectngle out the yxis. l in

7 8. Question Detils moment dy1 x^2 mod [ ] Find the moment of this region y following these steps. Assume the density of the region l is 1. in 2 1. Wht is the moment of the rectngle out the yxis? Write formul using x nd dx. l in 2. Ech rectngle genertes moment out the yxis. The moments cn e dded up with n integrl. Wht re the upper nd lower ounds of x for the region? 3. Set up the definite integrl to find the moment of the region out the yxis. 4. Compute your integrl using the Fundmentl Theorem of Clculus to determine the moment of the region out the yxis. (Do not use clcultor!) l in

8 9. Question Detils moment dy1 e^x [ ] Set up the definite integrl to find the moment of the region out the yxis. Assume the g density of the region is 1. (Use the steps from questions 7 & 8 if you re unsure of cm 2 wht to do.) where the ounds of integrtion re

9 10. Question Detils intro prts check [ ] The lst question involved n integrl of type tht you hve not yet lerned to evlute. f(x) = xe x is the product of two functions, ut usustitution won't work. You will lern how to evlute this type of integrl lter this semester.. Four students guess the ntiderivtive of f(x) = xe x Check ech student's guess y writing its derivtive. Alice guesses tht the ntiderivtive is F(x) = xe x. Check: Bo guesses tht F(x) = xe x e x. Check: Chris guesses tht F(x) = xe x + e x. Check: Dni guesses tht F(x) = x 2 e x. 2 Check:. Which of the four students re correct? Select ll tht pply. Alice Bo Chris Dni 11. Question Detils dy1 e^x definite [ ] Use the correct ntiderivtive from the previous question to compute the moment of the region from prolem #9 g cm Assignment Detils Nme (AID): 11 Bsic: Clc II Intro ( ) Sumissions Allowed: 100 Ctegory: Homework Code: Locked: Yes Author: Skriletz, Jimos ( jimosskriletz@oisestte.edu ) Lst Sved: Dec 10, :27 AM MST Group: BSU Clculus Rndomiztion: Person Which grded: Lst Feedck Settings Before due dte Question Score Assignment Score Pulish Essy Scores Question Prt Score Mrk Help/Hints Response Sve Work After due dte Question Score Assignment Score Pulish Essy Scores

10 Question Prt Score Mrk Add Prctice Button Help/Hints Response

n f(x i ) x. i=1 In section 4.2, we defined the definite integral of f from x = a to x = b as n f(x i ) x; f(x) dx = lim i=1

n f(x i ) x. i=1 In section 4.2, we defined the definite integral of f from x = a to x = b as n f(x i ) x; f(x) dx = lim i=1 The Fundmentl Theorem of Clculus As we continue to study the re problem, let s think bck to wht we know bout computing res of regions enclosed by curves. If we wnt to find the re of the region below the