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13 Nov 2019
f(x) dx = 12 and r(x) dx--2,find s: r(x) dr. 5. If 6. Justin wishes to estimate the integral rdx o 1 + cos x (i) Verify that the inequality-S1+ cos- 1 is valid on the interval [0, Ï, (ii) Use the inequality from part (i) to obtain the estimate Ï,Trax (ii) Use the inequality from part (i) to obtain the estimate 2 ) 1 + cos- Be sure to fully justify your reasoning for full credit (A continuation of problem #6.) Justin now gets the inspiration to do the following: He lets u = tan x with du = dx/cos2 x. Upon making the substitution, he finds that 7, r dx 1/cosx dx tan Ï du du where the final integral equals 0 since we are integrating over an interval of width 0 Comparing this to the result of problem 06, Justin eagerly concludes that 0 Make an argument that he is incorrect. Hint: Review carefully what Theorem 7 says. E Ï 8. Use the Riemann sum (rectangle) definition to evaluate (no credit awarded for using FT (x2 +2x-5) dx.
f(x) dx = 12 and r(x) dx--2,find s: r(x) dr. 5. If 6. Justin wishes to estimate the integral rdx o 1 + cos x (i) Verify that the inequality-S1+ cos- 1 is valid on the interval [0, Ï, (ii) Use the inequality from part (i) to obtain the estimate Ï,Trax (ii) Use the inequality from part (i) to obtain the estimate 2 ) 1 + cos- Be sure to fully justify your reasoning for full credit (A continuation of problem #6.) Justin now gets the inspiration to do the following: He lets u = tan x with du = dx/cos2 x. Upon making the substitution, he finds that 7, r dx 1/cosx dx tan Ï du du where the final integral equals 0 since we are integrating over an interval of width 0 Comparing this to the result of problem 06, Justin eagerly concludes that 0 Make an argument that he is incorrect. Hint: Review carefully what Theorem 7 says. E Ï 8. Use the Riemann sum (rectangle) definition to evaluate (no credit awarded for using FT (x2 +2x-5) dx.
Deanna HettingerLv2
9 Feb 2019