Higher Engineering Mathematics, Sixth Edition
382 Higher Engineering Mathematics y 0 6 12 18 123 x y 52 x^2 x y Figure 38.12 (b) (i) When the shaded area of Fig. 38.12 is rev ...
Some applications of integration 383 When areaPQRSis rotated about axisXXthe vol- ume generated is that of the pulley. The centr ...
384 Higher Engineering Mathematics Second moments of areas are usually denoted byIand have units of mm^4 ,cm^4 , and so on. Radi ...
Some applications of integration 385 C b x PG P G x l 2 l 2 Figure 38.16 maybedetermined.IntherectangleshowninFig.38.16, Ipp= bl ...
386 Higher Engineering Mathematics Table 38.1Summary of standard results of the second moments of areas of regular sections Shap ...
Some applications of integration 387 IPP=Ak^2 PP, from which, kPP= √ IPP area = √( 645000 600 ) =32.79mm Problem 13. Determine t ...
388 Higher Engineering Mathematics The centroid of a semicircle lies at 4 r 3 π from its diameter. Using the parallel axis theor ...
Some applications of integration 389 Problem 18. Determine correct to 3 significant figures, the second moment of area about axi ...
390 Higher Engineering Mathematics For rectangle F: IXX= bl^3 3 = ( 15. 0 )( 4. 0 )^3 3 =320cm^4 Total second moment of area for ...
Some applications of integration 391 2.0 cm 5.0 cm 3.0 cm (a) (b) (c) 15 cm 18 cm 10 cm 15 cm 5.0 cm L L Dia^5 4.0 cm Figure 38. ...
Chapter 39 Integration using algebraic substitutions 39.1 Introduction Functions which require integrating are not always in the ...
Integration using algebraicsubstitutions 393 be a lengthy process, and thus an algebraic substitution is made. Letu=( 2 x− 5 )th ...
394 Higher Engineering Mathematics Now try the following exercise Exercise 153 Further problems on integration using algebraic s ...
Integration using algebraicsubstitutions 395 Hence ∫ tanθdθ=ln(secθ)+c, since (cosθ)−^1 = 1 cosθ =secθ 39.5 Change of limits Whe ...
396 Higher Engineering Mathematics 3tan2t [ 3 2 ln(sec2t)+c ] 7. 2et √ (et+ 4 ) [ 4 √ (et+ 4 )+c ] In Problems 8 to 10, evalua ...
Revision Test 11 This Revision Test covers the material contained in Chapters 37 to 39.The marks for each question are shown in ...
Chapter 40 Integration using trigonometric and hyperbolic substitutions 40.1 Introduction Table 40.1 gives a summary of the inte ...
Integration using trigonometric and hyperbolic substitutions 399 Table 40.1Integrals using trigonometric and hyperbolic substitu ...
400 Higher Engineering Mathematics Problem 4. Evaluate ∫ π 3 π 6 1 2 cot^22 θdθ. Since cot^2 θ+ 1 =cosec^2 θ, then cot^2 θ=cosec ...
Integration using trigonometric and hyperbolic substitutions 401 ∫ π 4 0 4cos^4 θdθ= 4 ∫ π 4 0 (cos^2 θ)^2 dθ = 4 ∫ π 4 0 [ 1 2 ...
«
16
17
18
19
20
21
22
23
24
25
»
Free download pdf