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# Class Note for MATH 1431 with Professor Caboussat at UH 2

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This 25 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 16 views.

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Date Created: 02/06/15
MATH 1431 19328 J Alexandre Caboussat Lecture MWF 11AM 12PM Office hours MWF 12PM 1PM httpwwwmathuheduNcaboussatmath1431 httpwwwmathuheduNcaboussatmath1431 J MATH 1431 19328 J Alexandre Caboussat Lecture MWF 11AM 12PM Office hours MWF 12PM 1PM httpwwwmathuheduNcaboussatmath1431 httpwwwmathuheduNcaboussatmath1431 J If f is continuous on 37 b and a lt c lt b then ftdtbetdtAbftdt Area Area Total Area J METH 1411 When a lt b Consequence Let f be a continuous functions on 37 b The function F defined by X Fx ftdt is continuous on 37 b differentiable on 37 b and has derivative FX fx7 for all X 6 37 b Examples On the interval 01 If ft 1 Fx If ft t2 t1 Fx If ft sin5t Fx METH 1411 X 7r Compute tzisint2 dx and tzisint2dt 0 0 54 The Fund Imental Theorem of alculus HWTH 1431 Give a formula for the area bounded by the curve f 3 7X and the X aXis on the interval 721 Give a formula for the area bounded by the curve fx 2X3 7 X and the X aXis on the interval 721 Give a formula for the area bounded by the curve fx 2X3 7 X and the X aXis on the interval 721 1 Compute 2X37XdX b When f is not non negative fxdx represents the net area 3 area above the X aXis MINUS area below the X aXis Two types of questions b 0 Compute the net area fxdx 0 Compute the real geometric area between the graph of f and the X aXis Region I has area 2 region II has area 3 and region I has area 2 3 What is fxdx7 73 Region I has area 2 region II has area 3 and region I has area 2 1 What is fxdx7 73 Region I has area 2 region II has area 3 and region I has area 2 1 What is fxdx7 71 Region I has area 2 region II has area 3 and region I has area 2 What is the area bounded by the X aXis and the graph y fx Let s Remember Let f be continuous on 3 b A function G is called an anti derivative for f on 3 b if G is continuous on 3 b and GX fx for all X E 3 b In particular Fx ftdt is an anti derivative for f luliTl l 1431 1 The Fundamental Theorern of Calculus Let f be continuous on 37 b If G is any antiderivative for f on 37 b then bftdt Cb 7 63 METH 1411 Examples 4 Evaluate dex 1 Evaluate sintdt 0 4 Evaluate 537352s 1ds 1 Examples 1 2X Evaluate 0 de 1 1 Evaluate 7dr 0 t4 1 Function fx Antiderivative CX Xr sinx cosx sec2x secx tanx csc2x csc X cotx Xr1 r1 r rational number r 7 71 rmeH 1411 rmeH 1411 3 2X3 3X4 2sin5x dx 1 rmeH 1411 rmeH 1411

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