WebAssign Lesson 1-3a Substitution Part 1 (Homework)
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1 WeAssign Lesson -3 Sustitution Prt (Homework) Current Score : / 3 Due : Fridy, June 7 04 :00 AM MDT Jimos Skriletz Mth 75, section 3, Summer 04 Instructor: Jimos Skriletz. /.5 points Suppose you hve the tsk of finding the ntiderivtive: 3sin(4x + ) You cn trnsform this prolem into n esier prolem y following three step process. It strts with formul: u = 4x + Step. Find the derivtive of u. Write it in the form when you type in your nswer. u'. Be sure to include the differentil Step. Solve for. Your nswer will include the other differentil. = Step 3. Sustitute. There re two ovious moves. Replce with your nswer from Step. Replce (4x + ) with u. The result is new ntiderivtive prolem. Enter the new integrnd nd differentil elow. Note: Mny prolems sk you to stop here. Your finl nswer is trnsformed ntiderivtive prolem. You don't ctully find the ntiderivtive. If you re sked for solution, there re two more steps. Step 4. Find the new ntiderivtive. Write your nswer s formul involving u. Include + C. Step 5. In your nswer for Step 4, replce u with 4x +. 3sin(4x + ) =
2 . /.5 points Trnsform this ntiderivtive prolem using the sustitution u = x x 3 (x 4 + 0) 7 Step. Find du. Step. Solve for. = Step 3. Sustitute to crete new new ntiderivtive prolem, written in terms of u. Step 4. Find the new ntiderivtive. Write your nswer in terms of u nd include + C. Step 5. Solve the originl prolem. Write your nswer in terms of x nd include + C. x 3 (x 4 + 0) 7 = 3. / points Trnsform this ntiderivtive prolem using the sustitution u = 5x + 4. (5x + 4) 3 Your nswer must e new ntiderivtive prolem written in terms of u. Solve the originl prolem. Write your nswer in terms of x nd include + C (5x + 4) 3 =
3 4. / points Trnsform this ntiderivtive prolem using the sustitution u = sin x. sin 4 x cos x Your finl nswer should e new ntiderivtive prolem written in terms of u. Solve the originl prolem. Write your nswer in terms of x nd include + C sin 4 x cos x = 5. / points Trnsform this ntiderivtive prolem using the sustitution u = x. x e (x ) Your finl nswer should e new ntiderivtive prolem written in terms of u. Solve the originl prolem. Write your nswer in terms of x nd include + C x e x = 6. / points Trnsform this ntiderivtive prolem using the sustitution u = 5x +. x 5x + Your finl nswer should e new ntiderivtive prolem written in terms of u. Solve the originl prolem. Write your nswer in terms of x nd include + C x = 5x +
4 7. /3.5 points There is similr process for trnsforming definite integrl. cos πt dt Agin, the process strts with formul: u = πt Step. Find du. Step. Solve for dt. dt = Step 3. Mke the ovious sustitutions nd write new integrl, expressed entirely in terms of u Replce dt with your nswer from Step. Replce πt with u. But notice tht your new integrl hs unknown limits of integrtion. Step 4. Find new limits of integrtion y plugging the old limits into the sustitution formul. = u() = = u() = Note: Mny prolems sk you to stop here. Your finl nswer is trnsformed definite integrl. You don't ctully compute it. If you re sked to compute it you cn usully pply the Fundmentl Theorem to the new integrl. Use the fundmentl theorem to compute your new integrl. Write your nswer in exct (ut unsimplified) form. Do not use decimls. π π cos(u) du π/ = The nswer to the originl integrl is exctly the sme: cos dt πt =
5 8. /3.5 points Trnsform this integrl using the sustitution u = x 3 4. Step. Find du. x (x 3 4) 9 Step. Solve for. = Setp 3. Sustitute to crete new integrl. Write the integrnd nd differentil elow, expressed entirely in terms of u. Step 4. Find the new limits of integrtion. = Compute the new integrl. Write your nswer in exct (ut unsimplified) form. Do not use decimls. =
6 9. /3 points Trnsform this integrl using the sustitution u = 7x (7x + ) Your finl nswer should e new integrl written in terms of u. = nd = Compute the new integrl. Write your nswer in exct (ut unsimplified) form. Do not use decimls. 0. /3 points Trnsform this integrl using the sustitution u = cos x. π/ cos 3 x sin x 0 Your finl nswer should e new integrl written in terms of u. = nd = Then, compute the new integrl. Write your nswer in exct (ut unsimplified) form. Do not use decimls.
7 . /3 points Trnsform this integrl using the sustitution u =. x e ( /x ) x 3 Your finl nswer should e new integrl written in terms of u. = nd = Then, compute the new integrl. Write your nswer in exct (ut unsimplified) form. Do not use decimls.. /3 points Trnsform this ntiderivtive prolem using the sustitution u = x 0. x 0 x 0 Your finl nswer should e new integrl written in terms of u. = nd = Compute the new integrl. Write your nswer in exct (ut unsimplified) form. Do not use decimls.
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