082-Engineering-Mathematics-Anthony-Croft-Robert-Davison-Martin-Hargreaves-James-Flint-Edisi-5-2017

Review exercises 16 495
12 Given
14 Given
⎧
⎨t 2 v(t) =2ti+(3−t 2 )j+t 3 k
−2t2
h(t) = t
⎩
3 find
2<t3
∫ 1
4 3<t5
(a) vdt
0
evaluate
∫
∫ 2
2
(b) vdt
(a) h(t)dt
1
−1
∫
∫ 2
2.5
(c) vdt
(b) h(t)dt
0
0
∫ 4
15 Evaluate the following integrals:
(c) h(t)+1dt
∫
2
3
∫ 4
(a) |t|dt
−1
(d) h(t +1)dt
∫
0
2
∫ 2
(b) |t+2|dt
−3
(e) h(2t)dt
∫
−1
2
13 Ifa =ti−2tj+3tk,find ∫ 1
0 adt. (c) |3t −1|dt
0
Solutions
4 k<−1
5 (a) does notexist
(b) does notexist
(c) does notexist
(d) 1
(e) does notexist
6 k<0
7 (a) 2 (b) 14.7781 (c) 4
(d) 0.2 (e) 0
8 (a) 1 2
9 (a) 3 (b) −1 (c) 1
(d) 1 (e) 1
5
10 (a) 1 (b)
2
(d) 3 (e) 0.6
(c) 2.85
11 (a) 4.5 (b) 10.5 (c) 10
(d) 3 (e) 10
12 (a) 3
(b) 8.4323
(c) 22.25
(d) 26.5833
(e) 12.7917
13 0.5i −j+1.5k
14 (a) i+ 8 3 j + 1 4 k
(b) 3i + 2 3 j + 15
4 k
(c) 4i + 10
3 j+4k
15 (a) 5 (b) 8.5 (c)
13
3