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# Keyuan Liu Assignment Assignment9 due 03/04/2016 at 10:59pm PST 4. (1 pt) Improper Integrals, Innite Integrands: Compute the improper integrals...

Finish total 23 questions, just need the answers, no need the steps

Keyuan Liu Math3B-01-W16-Paul Assignment Assignment9 due 03/04/2016 at 10:59pm PST 1. (1 pt) Determine whether the integral is divergent or con- vergent. If it is convergent, evaluate it. If not, give the answer -1. Z 4 xe - 3 x dx Answer(s) submitted: (incorrect) 2. (1 pt) Find what value of c does R 5 c x 4 dx = 1 ? Answer: Answer(s) submitted: (incorrect) 3. (1 pt) Improper Integrals, Inﬁnite Limits of Integra- tion: Integrals may have inﬁnite limits of integration, or inte- grands that have singularities. Such integrals are called ”im- proper” even though there is nothing wrong with such integrals. They may have well deﬁned values, in which case we say they converge, or they may not, in which case we say they diverge. In this and the next problem, give the value of the integral if it converges, and enter the letter ”D” if it diverges. R 1 1 x 2 d x = . R 1 1 x d x = . R 1 e - x d x = . R 1 e x d x = . R - 1 1 + x 2 d x = . R π - e x d x = . Answer(s) submitted: (incorrect) 4. (1 pt) Improper Integrals, Inﬁnite Integrands: Com- pute the improper integrals below. Enter the letter ”D” if they diverge. R 1 0 1 x 2 d x = . R 1 0 1 x d x = . R 1 0 1 x d x = . R 1 0 ln x d x = . R 1 - 1 1 1 - x 2 d x = . Answer(s) submitted: (incorrect) 5. (1 pt) Determine whether the integral is divergent or con- vergent. If it is convergent, evaluate it. If not, state your answer as ”divergent”. Z - (( x + 3 ) 2 - 6 ) dx Answer(s) submitted: (incorrect) 6. (1 pt) The improper integral Z - xdx is A. convergent since the area to the left of x = 0 cancels with the area to the right of x = 0. B. convergent since it equals lim a →- Z 0 a xdx + lim b Z b 0 xdx = - + = 0. C. divergent since both integrals Z 0 - xdx = - and Z 0 xdx = + are divergent. D. divergent by comparison to Z - xe - x dx . 1
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