Solution b True by Theorem 735 732 True or false a If f is bounded on a b then

# Solution b true by theorem 735 732 true or false a if

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Solution: (b) True by Theorem 7.3.5.7.3.2 True or false:(a) Iffis bounded on[a, b], then the proper integral offon[a, b]and theimproper integral offon(a, b)are equal.(b) Supposefis defined on[a, b]and integrable on[c, d]for everyc(a, b]. IflimcaRbcfdoes not exist, then the improper integralRbafis said to diverge. 7.3.5. Use Theorem 7.3.1 to find a formula for the derivative of each function.1 +t2dt. Solution:
(d) SinceF(x) =Rx30x200F0(x) =p1 + (x3)2·3x2-p1 + (x2)2·2x.7.3.17. Find the value of eacn improper integral, provided it is finite. Solution: Prove the following:1.Iff0(x) = 0for allx(a, b), thenfis a constant. 179

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