MAT136H1 Chapter Notes - Chapter 5.5: Differentiable Function
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MAT136H1 Full Course Notes
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Change the limits of integral after substitution. The substitution rule : if =(cid:1859)(cid:4666)(cid:4667) is a differentiable function whose range is an interval and (cid:1858) is continuous on , then (cid:1858)(cid:4666)(cid:1859)(cid:4666)(cid:4667)(cid:4667)(cid:1859) (cid:4666)(cid:4667)= (cid:1858)(cid:4666)(cid:4667). When evaluating a definite integral, 2 methods are possible : compute the indefinite integral first, then apply . The substitution rule for definite integrals : if (cid:1859) is continuous on [(cid:1853),(cid:1854)] and (cid:1858) is continuous on the range of =(cid:1859)(cid:4666)(cid:4667), then (cid:1858)(cid:4666)(cid:1859)(cid:4666)(cid:4667)(cid:4667) (cid:1859) (cid:4666)(cid:4667)= (cid:1858)(cid:4666)(cid:4667) (cid:4666)(cid:3029)(cid:4667) (cid:4666)(cid:3028)(cid:4667) Integrals of symmetric functions : suppose (cid:1858) is continuous on [ (cid:1853),(cid:1853): if (cid:1858) is even [(cid:1858)(cid:4666) (cid:4667)=(cid:1858)(cid:4666)(cid:4667)], then (cid:1858)(cid:4666)(cid:4667) =2 (cid:1858)(cid:4666)(cid:4667) (cid:3028) (cid:3028) (cid:3028)0: if (cid:1858) is odd [(cid:1858)(cid:4666) (cid:4667)= (cid:1858)(cid:4666)(cid:4667)], then (cid:1858)(cid:4666)(cid:4667)