Matematicas

1. EXAMEN FINAL DE MATEMATICAS DE LA 4ta UNIDAD
Guillermo Osban Casas Santoyo 1° ”C”
1.- ∫ ퟓ풙ퟐ 퐬퐢퐧 ퟓ풙ퟑ 풅풙 =
ퟓ
ퟏퟎ
∫ 퐬퐢퐧 ퟓ풙ퟐ .ퟏퟎ풙풅풙
v = ퟓ풙ퟐ =
5
10
(− cos 5푥 2 ) + 퐶
dv = ퟏퟎ풙풅풙 = −
5
10
cos 5푥 2 + 퐶
2.- ∫
풙ퟑ
ퟓ
풔풆풄ퟐ ퟓ풙ퟒ풅풙 =
풙ퟑ
ퟐퟎ
∫ 퐬퐞퐜 ퟓ 풙ퟒ . ퟐퟎ 풙ퟑ풅풙
v = ퟓퟒ =
푥3
20
cot 5푥 4 + 퐶
dv = ퟐퟎ풙ퟒ풅풙
3.- ∫
풙
ퟓ
퐬퐞퐜 ퟓ풙ퟐ풅풙 =
풙
ퟏퟎ
∫ 풔풆풄 ퟓ풙ퟐ . ퟏퟎ풙풅풙
v = ퟓ풙ퟐ =
푥
ln (sen 5푥 2 tan 10 푥푑푥) + 퐶
10
dv = ퟏퟎ 풙풅풙 =
푥
푠푒푛 5푥 2 tan 10 푥푑푥 + 퐶
10

2. 4.- ∫
ퟓ풙ퟓ 풅풙
풆풙ퟓ =
ퟓ
ퟒ
∫ 풆−풙ퟓ(−ퟓ) 풙ퟒ풅풙
v = -풙ퟓ =
−5
4
푒−푥5 + 퐶
dv = -ퟓ풙ퟒ풅풙 =
−5
4푒푥5 + 퐶
5.- ∫
풙ퟐ
ퟓ
풔풆풄ퟓ풙ퟑ 퐭퐚퐧 ퟓ풙ퟑ풅풙 =
풙ퟐ
ퟕퟓ
∫ 퐬퐞퐜 ퟓ풙ퟑ . 퐭퐚퐧 ퟓ풙ퟐ . ퟏퟓ풙ퟐ풅풙
v = ퟓ풙ퟑ =
푥2
75
sec 5푥 3 + 퐶
dv = ퟏퟓ풙ퟐ풅풙
6.- ∫
ퟓ풙ퟐ 풅풙
(ퟓ)ퟐ−풙ퟖ =
ퟏ
ퟐ(풂)
퐥퐧
ퟏퟎ+풙ퟒ
ퟏퟎ−풙ퟒ + 푪
풗ퟐ = (풙ퟒ)ퟐ ∴ v = 풙ퟒ =
1
10
ln
10+푥4
10−푥4 + 퐶
푎2 = (5)2 ∴ a = 10

3. 7.- ∫
풙ퟒ 풅풙
ퟓ풆풙ퟓ =
ퟓ
ퟓ
∫ ퟓ풆−풙ퟓ(−ퟓ)풙ퟒ풅풙
v = -풙ퟓ =
−5
5
푒−푥5 + 퐶
dv = −ퟓ풙ퟒ풅풙 =
−5
5푒푥5 + 퐶
8.- ∫ 풙ퟐ√ퟗ − 풙ퟑ 풅풙 = ∫ √(ퟗ)ퟐ − (풙)ퟑ풅풙
풗ퟐ = (풙)ퟑ ∴ v = 풙ퟑ =
푥3
2
√(9)2 − (푥)3 + (9)2푎푟푐 sin
푥3
81
+ 퐶
풂ퟐ = (ퟗ)ퟐ ∴ a = 81 =
푥3
2
(81 − 푥 3 )
1
2 +
81
2
푎푟푐 sin
푥3
81
+ 퐶