Higher Engineering Mathematics, Sixth Edition
362 Higher Engineering Mathematics Following the procedure: (i) ∂z ∂x = 2 (x^2 +y^2 ) 2 x− 16 x and ∂z ∂y = 2 (x^2 +y^2 ) 2 y+ 1 ...
Maxima, minima and saddle points for functions of two variables 363 y x z^5 0 z (^5128) z^59 h g c d 22 2 222 a S f b e j i 24 4 ...
364 Higher Engineering Mathematics Letz=f(x,y)=x^3 − 3 x^2 − 4 y^2 +2. Following the procedure: (i) ∂z ∂x = 3 x^2 − 6 xand ∂z ∂y ...
Maxima, minima and saddle points for functions of two variables 365 z x y Figure 36.11 Let the dimensions of the container bex,y ...
366 Higher Engineering Mathematics Determine the stationary points of the surface f(x,y)=x^3 − 6 x^2 −[y^2. Maximum at (0, 0), ...
Revision Test 10 This Revision Test covers the material contained in Chapters 32 to 36.The marks for each question are shown in ...
Chapter 37 Standard integration 37.1 The process of integration The process of integration reverses the process of differentiati ...
Standard integration 369 For example, ∫ ( 3 x+ 2 x^2 − 5 )dx = ∫ 3 xdx+ ∫ 2 x^2 dx− ∫ 5dx = 3 x^2 2 + 2 x^3 3 − 5 x+c 37.3 Stand ...
370 Higher Engineering Mathematics (b) Rearranging ∫ ( 1 −t)^2 dtgives: ∫ ( 1 − 2 t+t^2 )dt=t− 2 t^1 +^1 1 + 1 + t^2 +^1 2 + 1 + ...
Standard integration 371 Problem 9. Determine (a) ∫ 7sec^24 tdt (b) 3 ∫ cosec^22 θdθ. (a) From Table 37.1(iv), ∫ 7sec^24 tdt=( 7 ...
372 Higher Engineering Mathematics (a) ∫ 3cos2xdx (b) ∫ 7sin3θdθ ⎡ ⎢ ⎢ ⎣ (a) 3 2 sin2x+c (b)− 7 3 cos3θ+c ⎤ ⎥ ⎥ ⎦ (a) ∫ 3 4 ...
Standard integration 373 = ⎡ ⎣θ 3 2 3 2 + 2 θ 1 2 1 2 ⎤ ⎦ 4 1 = [ 2 3 √ θ^3 + 4 √ θ ] 4 1 = { 2 3 √ ( 4 )^3 + 4 √ 4 } − { 2 3 √ ...
374 Higher Engineering Mathematics (a) ∫ 2 1 cosec^24 tdt (b) ∫ π 2 π 4 (3sin2x−2cos3x)dx [(a) 0.2527 (b) 2.638] (a) ∫ 1 0 3 ...
Chapter 38 Some applications of integration 74.1 Introduction There are a number of applications of integral calculus in enginee ...
376 Higher Engineering Mathematics Problem 2. Determine the area enclosed between the curvesy=x^2 +1andy= 7 −x. At the points of ...
Some applications of integration 377 Sketch the curvesy=x^2 +3andy= 7 − 3 x and determine the area enclosed by them. [20^56 squ ...
378 Higher Engineering Mathematics In this case, r.m.s. value= 1 √ 2 × 100 = 70 .71V] Now try the following exercise Exercise 14 ...
Some applications of integration 379 Problem 6. Determine the area enclosed by the two curvesy=x^2 andy^2 = 8 x.Ifthisareais rot ...
380 Higher Engineering Mathematics 38.5 Centroids Alaminais a thin flat sheet having uniform thickness. Thecentre of gravityof a ...
Some applications of integration 381 = 625 3 − 625 4 125 2 − 125 3 = 625 12 125 6 = ( 625 12 )( 6 125 ) = 5 2 =2.5 y= 1 2 ∫ 5 0 ...
«
15
16
17
18
19
20
21
22
23
24
»
Free download pdf