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Examen 4 unidad matematicas integrales
- 1. 1. ∫26풙ퟐ풔풆풏 ퟐퟔ풙ퟑ풅풙 =
26
52
∫ Sen 26푥2• 52푥2푑푥
26
52
(– 푐표푠26푥2) + 푐
26
52
cos 26 푥2 + 푐
ퟐ. ∫
풙ퟑ
ퟐퟔ
풔풆풄ퟐ ퟐퟔ풙ퟒ 풅풙 =
푣 = 26푥2
푑푣 = 104푥3푑푥
푥3
104
∫ 푠푒푐2 26푥4• 104푥2 푑푥
푥3
104
푡푎푛 26푥4 + 퐶
3.∫
풙
ퟐퟔ
풔풆풄ퟐퟔ풙ퟐ풅풙 =
푣 = 26푥2
푑푣 = 52푥 푑푥
- 2. 푥
52
∫ sec 26푥2• 26푥2•52푥 푑푥
푥
52
푙푛 (푠푒푐26푥2+tan 26푥2)
푥
52
푙푛 푠푒푐 26푥2+ 푡푎푛 26푥2+ 퐶
ퟒ. ∫
ퟐퟔ풙ퟐퟔ풅풙
풆풙ퟐퟔ =
26
27
∫ 푒−푥27
(−27)푥26 푑푥
푣 = −푥27
푑푣 = −27푥26
−
26
27
∫ 푒푥26 + 퐶
−26 푒−27
27
+ 퐶
5.∫
풙ퟐ
ퟐퟔ
풔풆풄 ퟐퟔ풙ퟑ풅풙 =
- 3. 26
78
∫ 푠푒푐26푥3 • tan 26푥3 • 78푥2푑푥
푣 = 26푥3
푑푣 = 78푥2푑푥
26
78
sec 26푥3 + 퐶
6. ∫
ퟐퟔ풙ퟑ
(ퟐퟔ)ퟐ−풙ퟖ 풅풙 =
1
2(78)
푙푛
78+푥4
78−푥4 + 퐶
푣2 = (푥4)2 a=(3)2
푣 = 푥4 푎 = 푎
푑푣 = 4푥3푑푥
−1
ln
(2)52
52 − 푥4
52푥4 + 퐶
- 4. 7. ∫
풙ퟒ풅풙
ퟐퟔ풆풙ퟓ=
26
5
∫ 푒−푥5 • 5푥4푑푥
푣 = 푥5
푑푣 = 5푥4푑푥
26
5
푒−푥4
+ 퐶
8. ∫ 풙ퟐ √(ퟗ) − 풙ퟑ풅풙 =
∫ √(9)2 − (푥)3푑푥
푣2 = (푥)3
푣 = 푥3
푑푣 = 3푥2푑푥
푎2(9)2
푎 = 81
- 5. 푥3
2
= √(9)2 − (푥)3 +
(9)2
2
푎푟푐 푠푒푛
푥3
81
+ 퐶
푥3
2
√81 − 푥3 +
81
2
푎푟푐 푠푒푛
푥3
81
+ 퐶
푥3
2
(81 − 푥3)
1
⁄2 +
81
2
푎푟푐 푠푒푛
푥3
81
+ 퐶