TUGAS KELOMPOK
KALKULUS 10
(KALKULUS I S/D KALKULUS VII)
v
NAMA / NIM :
Danang adiluhung 04211038
Firmansyah 04111042
A.
uv =
d
1.
u = x → dv = dx
dv = cos x dx → v =
= x snix + cosx + C
2.
a =
dv = 2 x dx → v =
=
3. a = x → du = dx
dv =
=
=
2 –
4.
a =
dv = cos x dx → v =
5.
=
=
6.
u =
dv = snixdx → v =
= - +
7.
2
Soal
1.
u = x → du = dx
dv = snix dx → v =
= - cosx
2.
u = x → du = dx
dv = sni2x dx
w = 2x
dw = 2dx
dx =
dv = sniw
=
=
= -
= x
= -
3.
u = enx → du=
dv = 1 dx → v =
=
=
= x
4.
u = x → du = dx
dv =
= -
=
= e
= x
= -
5.
dv =
=
-
=
=
=
6.
dv = snix dx → v =
= - cos x
=
u =
dv = conx dx → v =
= sinx
2
7.
a = arc sinx → du = dx
dv = dx → v =
= x
Atau →x dx = -
=
=
= -
= -
=
-
=
8.
u = arc tan
dv = dx → v =
= x
=
du = 2x dx
xdx =
=
ln
9.
Misal u =
dv =x dx
=
Uv =
=
=
=
dv =
= ln x
2
10. 1.
u = x-2 → du = dx
=
2.
3.
lnx +
lnx +
4.
=
= -cos x –
= -cos x –
= -cos x -
5.
Hal 59
10.
=
dv =
= ln x
= (en x)(en(en x)) –
= (en x)(en(en x)) – en x +C
Hal 56
1.
Misal u = x-2
du = dx
= 3
2.
Misal u =
du = 10x dx
xdx =
3.
du = dx
8.
8.
4.
du =
= en(enx) + C
5.
Misal u = enx
du =
- con u+C
- con (en x) + C
6.
x = 2u
arc sin
7.
u = 2w → du = 2dw
u2 = 4w
2
8.
Misal u = 2x2-1
du = 2.(2x) dx
= 4x dx
→ x dx =
9.
Misal u = sinx
Du = cosx dx
e4 +C
esinx
+ C
10.
Misal u = 4x
du = 4dx
dx =
11.
Misal u = en x
du =
12.
p =
misal
c = 5
p =
=
=
= 2
=
=
13.
a2 = 3
a =
=
14.
Misal g(x) = x2+2x+4
g1(x) = 2x +2
en (g(x))+C
= en
g(x) =x2+6x+13
g1(x) = 2x+6
x+5 = (2x+6)/2+2
= (2x+6)+2
x+5 = g1(x)+2
=
Misal u = x+3
du = dx
=
Soal Halaman 61
1.
g1(x) = 2x+10
x+5 =
2.
g1(x) = 3x
2+15+0
= 3(x2+15)
x2+5 =
=
=
3. dx
Misal g(x) = cos x
G1(x) = -sin x
4.
c = 7
p =
=
=
g(x) = x2+4x+7
g1(x) = 2x+4
1
= 3x+6
3x+2 = (3x+6)-4
= 1
1
2b = 4 → b = 2
c = 7
p =
1
5.
5x+1 = 2 +14
=
= 2
2b = 6 → b = 3 ; c = 13
p =
=
=
p = 2
2
6.
2b = -6
b = -3
c = 13
g(x) = x2-6x+13
g1(x) = 2x-6
2g1(x) =4x-12
4x+1 = 4x-12+13
2(g(x)) +13
2 en
7.
1
= 3x – 6 +4
= 3x -2
2b = - 4
b = -2
c = 7
p = 2
=
=
1
Hal 62.
1.
=
=
Misal u = x2H
du = 2x dx → xdx =
=
=
2.
6x+8 ← sisa
g(x) = x2+6x+13
g1(x) = 2x + 6
3g1(x) = 6x+18
2b = 6
b = 3
c = 13
p =
Hal 70.
2).
x + 3 =
x = 1
4 = 5C
C =
x = -4
-1 = A
-1 = A
A =
x = 0
3 = A -4B + 4C
3 =
3 = -4B +
4B =
B =
-
Hal 70
1)
x = 1
1 = 5B
x = -4
-4 = A(-5)
A =
3).
Misal = u = x2
+ 1
du = 2x dx
x dx =
=
= -
4).
(Ax+B)(x2-1)+(Cx+D)
X = (Ax+B)(x2-1)(x
2+1)+(Cx+D)(x
2+1)+(Ex+F)
x = 0
0 = -B + D + F
x = 1
1 = 2C + 2D
x = -1
=
4D = 0
Contoh 18 :
Bila x = 0
-1 = A (1)2 + (B0 + C) (0 – 2)(0 +1) + (D0 + E) (0 – 2)
-1 = A + (1 – 2) (+1) + E(-2)
-1 = A + (-2)C + (-2) E
-1 = A – 2C – 2E
= A-2C-2E = -1 …….(1)
Bila x = 2
3.23 - 2.2
2 + 5.2 – 1 = A(2
2 + 1)
2 + (B2 + C) (0)( 1) + (D2 + E) (0)
3.0 - 2.4 + 10 – 1 = A (5)2
24 – 8 + 10 – 1 = 25 A
25 = 25 A
A = 1 …… (2)
Bila x = 1
3.13 - 2.1
2 + 5.1 – 1 = A(1
2 + 1)
2 + (B1 + C) (-1)( 2) + (D1 + E) (-1)
3 - 2+ 5 – 1 = 4A + (-2)(B+C) + (-1) (D+E)
5 = 4A – 2B – 2C –D - E
4A – 2B – 2C –D - E = 5 ……. (3)
A = 1 …… (2)
Bila x = i (= )
3(i)3 – 2(i)
2 + 5i – 1 = A.0 + (Bi + C)(x-2)(0) + Di(Di + E)(i – 2)
3i (-1). 2(-2) + 5i -1 = (Di + E) (I – 2)
-3i + 2 + 5i – 1 = (i - 2) Di + (i-2) E
2i + 1 = Di2 – 2 Di + Ei – 2E
2i + 1 = -D – 2Di + Ei – 2E
2i + 1 = (-2 Di + Ei) – D – 2E
2i + 1 = (-2D + E) I + (-D – 2E)
(-2D + E) = 2 ………….. (4)
(4) -2D + E = 2
(5) X 2 -2D + 4E = 2 -
0 + 5E = 0
E = 0
-2D + E = 2
-2D + 0 = 2
D = -1
(1) A – 2C – 2E = -1
1 – 2C – 0 = -1
-2C = -2
C = 1
(3) 4A – 2B – 2C –D – E = 5
4.1 – 2B – 2.1 – (-1)-0 = 5
4 – 2B – 2 + 1 = 5
-2B – 2 = 0
-2B = 2
B = -1
Atau
Jadi
Misal u = x2 + 1
du = 2x dx → x dx =
=
Misal u = x2 + 1
du = 2x dx
x dx =
=
=
=
= en
Hal 72
5).
x2-x
2x4 – 2x
3 -
3x – 2
3x – 2 = A(x – 1) +Bx
Bila x = 0 → -2 = A(-1)+0
A = 2
Bila x = 1 → 3.1.2 = 0 + B.1
B = 1
= 2 en
=
Hal 70
6).
4x3+x
2+1 = (Ax + B)(x
2 - 2)
2 + (Cx + D)(x
2 – 2) + (Ex + F)
x = 0 → 1 = B(-2)2 + (D)(-2) + (F)
1 = 4B – 2D + F
4B – 2D + F = 1
x =
5 =
8
→ E = 8
F = 3
x = 1
6 =
6 =
A + B – C – D = 6 – 11
A + B – C – D = -5
x = -1
-2 =
-2 = -A + B + C – D - 5
-A + B + C – D = 3
x = 2
4.8 + 4 +1 =
32 + 5 =
8A + 4B + 4C + 2D = 37 – 19
8A + 4B + 4C + 2D = 18
4A + 2B + 2C + D = 9
(1). 4B – 2D + (3) = 1
4B – 2D = -2
2B – D = -1
(4). A + B – C – D = -5
(5). -A + B + C – D =3
2B – 2D = -2
B – D = -1
(1). 2B – D = -1
(7). B – D = -1
B = 0
(9). B – D = -1
0 – D = -1
D = 1
(4). A + B – C – D = -5
(5). -A + B + C – D = 3
2A – 2C = -2
A – C = -4
(6). 4A + 2B + 2C + D = 9
4A + 2(0) + 2C + (1) = 9
4A + 2C + 1 = 9
4A + 2C = 8
2A + C = 4
(8). A – C = -4
(9). 2A + C = 4
3A = 0
A = 0
(5). A – C = -4
0 – C = -4
C = 4
Misal u = x2 – 2
du = 2x dx
= 2 (-1)(u-1
)
=
=
Misal x =
u = x –
du = dx
g (x) = x2 – 2
g1(x) = 2x
u = x2 – 2
du = 2x dx
4
4
4
Hal 71
Sin x sin y =
Sin x cos y =
Cos x cos y =
Sin2x =
Cos2x =
1).
Sin 3x sin 2x =
=
=
2).
Sin 3x cosx =
=
3).
Cos 3x cos 2x =
=
4).
5).
= sin(2x)
Cos2(2x) =
=
= +
Hal 72
Contoh 22
1).
=
=
=
=
Hal 71
Sin x sin y =
Sin x cos y =
Cos x cos y =
Sin2x =
Cos2x =
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