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Examen unidad 4
- 1. 1) ∫ 10푋2 푠푒푛 10 푥 3푑푥=
10
30
∫ 푠푒푛 10 푥 3. 30푥 2 푑푥
V= 10푥 3
dv= 30푥 푑푥 =
10
30
(− cos 10 푥3 ) + 푐
=
10
30
cos 10푥 3 + 푐
2) ∫ 푥3
10
푠푒푐2 10 푥 4 푑푥 = 푥
20
∫ 푠푒푐2 10 푥 4 40푥3 푑푥
V= 10푥 4
Vd= 40푥 3 푑푥 =
푥3
40
+ 푎푛 10 푥 4 + 푐
3)
푥
10
sec ∫ 10 푥 2 푑푥 =
푥
20
∫ sec 10 푥 2. 10 푥 2 − 20 푥 푑푥
V= 10 푥2 =
푥
20
퐼푛(sec 10 푥 2 + (tan 10푥 2) + 푐
Vd= 20 x dx =
푥
20
퐼푛 sec 10 푥 2 + tan 20 푥2 + 푐
4) ∫
10 푥10 푑푥
푒푥10 +1 =
10
11
∫ −푒 (11)푥10 푑푥
V= 푥 11 =
−10
11
푒 푥11 + 푐
dv= 11 푥 10 푑푥
- 2. 5) ∫ 푥2
10
sec 10 푥3 . tan 10 푥 3 푑푥 =
푥2
10
∫ sec 10 푥 3 . tan 10 푥 3 . 30 푥 2 dx
V= 10 푥3 =
푥2
30
sec 10 푥3 + 푐
dv=30 푥2 푑푥
6) ∫
10푥3
(10)2 −푥8
= ∫ 4푥 3 푑푥
102 −( 푥4 )2 = 1
2(20)
퐼푛 20− 푥4
20+ 푥4 + 푐
푣2 = ( 푥4)2 푎2 = ( 10 )2
1
40
퐼푛 20 − 푥4
20 + 푥4 + 푐
V= 푥 4 푎 = 20
7) ∫ 푥4 푑푥
10 푒 푥5=
− 푥4
5
∫ - e 푥 5(5)푥 4푑푥
V= 푥 5 = − 푥4
5
푒 푥 5 + 푐
dx=5푥 4푑푥
8) ∫ 푥 2√9 − 푥 3 푑푥 = 푥3
2
√(9)2 − (푥)3 +
(9)2
2
푎푟푒 푠푒푛 푥3
81
푣2 = (푥)3 푎2 = (9)2 = 푥3
2
√(9)2 − (푥)3 +
(9)2
2
푎푟푒 푠푒푛 푥3
81
+ 푐
푣 = 푥 3 a= 81
Vd = 3푥 2 푑푥 = 푥3
2
( 82 − 푥 3)
1
2 + 81
2
푎푟푒 푠푒푛 푥3
81
+ 푐