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Tugas kisi2 10 soal
1.
TUGAS MATEMATIKA Kisi-Kisi Test
Akhir Semester 2 MTK2 Di susun oleh : Nama : Gesti Kelas : 1 ElektronikaB Semester : 2 (Genap) Jurusan : Elektronikadan Informatika POLITEKNIK MANUFAKTUR NEGERI BANGKA BELITUNG Kawasan Industri Air Kantung Sungailiat 33211 Bangka Induk Propinsi Kepulauan Bangka Belitung Telp : (0717) 431335 ext. 2281, 2126 Fax : (0717) 93585 email : polman@polman-babel.ac.id http://www.polman-babel.ac.id/ 1 . ∫(𝑥10 − 6 𝑥5 + √𝑥73 ) 𝑑𝑥 = ∫(𝑥10 − 6𝑥−5 + 𝑥 7 3) 𝑑𝑥
2.
= 1 11 𝑥11 + 6 4 𝑥−4 + 3 10 𝑥 10 3
+c = 1 11 𝑥11 + 3 2 𝑥−4 + 3 10 𝑥 10 3 +c 2. ∫[cos(9𝑥 − 11) + 𝑠𝑒𝑐2(6𝑥 − 8)] 𝑑𝑥 = 1 9 sin(9𝑥 − 11) + 1 6 tan(6𝑥 − 8) + 𝑐 3. Denganmenggunakancara subsitusi ∫ 𝑥 √6+𝑥2 𝑑𝑥 =∫ 𝑥(6 + 𝑥2) 1 2 𝑑𝑥 Misalkan : 𝑢 = 6 + 𝑥2 𝑑𝑢 𝑑𝑥 = 2𝑥 𝑑𝑢 = 1 2𝑥 𝑑𝑢 ∫ 𝑥(6 + 𝑥2) 1 2 𝑑𝑥 =∫ 𝑥 𝑈 −1 2 . 1 2𝑥 𝑑𝑢 =∫ 𝑥 2𝑥 . 𝑈 −1 2 𝑑𝑢 =∫ 1 2 . 𝑈 −1 2 𝑑𝑢 = 1 2 −1 2 +1 𝑈 −1 2 +1 + 𝐶 = 1 2 1 2 𝑈 1 2 + 𝐶 =(6𝑥 + 𝑥2) 1 2 + 𝐶 4. Denganmenggunkancara subsitusi
3.
∫(2𝑥 + 5)cos(2𝑥2
+ 10𝑥 + 8 ) 𝑑𝑥 Misalkan U =2𝑥2 + 10𝑥 + 8 𝑑𝑢 𝑑𝑥 = 4𝑥 + 10 Dx= 1 4𝑥+10 𝑑𝑢 ∫(2𝑥 + 5)cos(2𝑥2 + 10𝑥 + 8 ) 𝑑𝑥 =∫(2𝑥 + 5)cos 𝑢 1 4𝑥+10 du ∫ (2𝑥+5) 2 (2𝑥+5) cos 𝑢 𝑑𝑢 ∫ 1 2 cos u du = 1 2 sinu du = 1 2 sin(2𝑥 2+ 10x +8 ) + c 5. Integral parsial ∫2𝑥. sin(10𝑥 + 3) dx Misalkan: u= 2x du =2dx dv =sin(10x +3 ) v=∫sin(10𝑥 + 3) 𝑑𝑥 = − 1 10 cos(10𝑥 + 3) =∫ 𝑈𝑑𝑣 = 𝑢𝑣 −∫ 𝑣 𝑑𝑢 =∫2𝑥.sin(10𝑥 + 3) 𝑑𝑥 =2𝑥 (− 1 10 cos(10𝑥 + 3)) − ∫− 1 10 cos(10𝑥 + 3). 2 𝑑𝑥 =− 1 5 𝑥.cos(10𝑥 + 3) 𝑑𝑥 + 2 100 sin(10𝑥 + 3) + 𝐶 =− 1 5 𝑥.cos(10𝑥 + 3) + 1 50 sin(10𝑥 + 3) + 𝐶
4.
6. Denganmenggunakantable ∫ 𝑥2
𝑒−7𝑥 𝑑𝑥 Turunan U Integral dv +𝑥2 -2x +2 -0 𝑒−7𝑥 − 1 7 𝑒−7𝑥 1 49 𝑒−7𝑥 − 1 363 𝑒−7𝑥 ∫ 𝑢𝑑𝑣 = 𝑥2 ( − 1 7 𝑒−7𝑥) -2x . 1 49 𝑒−7𝑥 + 2 (− 1 369 𝑒−7𝑥)+ 𝑐 = −𝑥2 1 7 𝑒−7𝑥 -2x . 1 49 − 2 363 𝑒−7𝑥 𝑒−7𝑥 + 2 + 𝑐 = − 1 7 𝑥2 𝑒−7𝑥 -2x . 1 49 − 2 363 𝑒−7𝑥 𝑒−7𝑥 + 2 + 𝑐 7.Integral fungsi rasional ∫ 𝑥 𝑥2−2𝑥−35 𝑑𝑥 𝑥 𝑥2−2𝑥−35 = 𝑥 ( 𝑥−7)(𝑥+5) = 𝐴 (𝑥−7) + 𝐵 (𝑥+5) = 𝐴( 𝑥+5)+𝐵(𝑥−7) ( 𝑥−7)( 𝑥+5) 𝐴𝑥+5𝐴+𝐵𝑥−7𝐵) ( 𝑥−7)( 𝑥+5) A+B = 1 x5 5A+5B = 5 5A +B =0 x1 5A-7B = 0 12B=5 B= 5 12 A= 7 12
5.
Sehingga: ∫ 𝑥 ( 𝑥−7)(𝑥+5) 𝑑𝑥 =
∫ 𝐴 ( 𝑥−7) 𝑑𝑥 + ∫ 𝐵 ( 𝑥+5) 𝑑𝑥 =∫ 7 12 ( 𝑥−7) 𝑑𝑥 + ∫ 5 12 ( 𝑥+5) 𝑑𝑥 = 7 12 𝑙𝑛 x-7 + 5 12 𝑙𝑛 x+5 + C 8.∫ ( 𝑥45 1 + 3𝑥 + 1 𝑥3 ) 𝑑𝑥 =∫ ( 𝑥45 1 + 3𝑥 + 𝑥−3 ) 𝑑𝑥 = 1 5 [𝑥5 + 3 2 𝑥2 − 1 2 𝑥−2]5 1 = ( 1 5 55 + 3 2 52 − 1 2 𝑥5−2 ) –( 1 5 15 + 3 2 12 − 1 2 1−2 ) =(625 + 75 2 − 1 50 ) − ( 1 5 + 3 2 − 1 2 ) =625- 1 + 75 2 − 1 50 − 1 5 =624 + 75 2 - 1 50 - 1 5 31200 + 1875 − 1 − 10 50 = 33064 50 = 661 14 50 9.Dik = y = 𝑥2 − 1 Y = 3x + 9 Dit = Luas daerah Jawab: 𝑥2 − 1 = 3𝑥 + 9 𝑥2 − 1 − 3𝑥 − 9 = 0 𝑥2 − 3𝑥 − 10 = 0 (x-5) (x+2) = 0 X= 5 v x=-2
6.
L=∫ (3𝑥 +
9 )– (𝑥25 −2 − 1) 𝑑𝑥 =∫ 3𝑥 − 5 −2 𝑥2 + 10 𝑑𝑥 = 3 2 [𝑥2 − 1 3 𝑥3 + 10𝑥] 5 −2 =( 3 2 52 − 1 3 53 + 10.5) − ( 3 2 (−2)2 − 1 3 (−2)3 + 10. −2) = ( 75 2 − 125 3 + 50) − (6 + 8 3 − 20) = ( 225−250+300 6 ) − ( 18+8−60 3 ) = 275 6 + 34 3 = 275+68 6 = 343 6 = 57 1 6 10. Diketahu : iy= 3x Y= x Y= 0 y= 2 Dit : Volume benda =mengelilingi sumbuy Jawab= V = 𝜋 ∫ ( 𝑥2 − 𝑥22) 𝑑𝑦 𝑑 𝑒 = 𝜋∫ (𝑦2 − ( 2 0 1 3 𝑦)2 ) dy = 𝜋∫ 𝑦2 − 2 0 1 9 𝑦2 dy = 𝜋∫ − 2 0 8 9 𝑦2 dy =𝜋[( 8 9 2+1 𝑦2+1)] 2 0 = 𝜋( 8 27 𝑦3) 2 0 = 𝜋( 8 27 23-)-( 8 27 . 03) = 𝜋 64 27 =2 10 27 𝜋
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