اﻟﺘﻜﺎﻣـــــﻞ
اﻟﺜﺎﻧﻴﺔ ﺳﻠﻚ ﺑﻜﺎﻟﻮرﻳﺎ ﻋﻠﻮم ﺗﺠﺮﻳﺒﻴﺔ
ﺗﻤﺎرﻳﻦ و ﺣﻠﻮل 4ﺗﻤﺮﻳﻦ
1 1 1 ﺗﺄآﺪ أن/ أ-1 − = t t + 2 t (t + 2)
dt
2
∫1 t ( t + 2 ) dt أﺣﺴﺐ/ب π
∫02 e π
x
sin xdx
أﺣﺴﺐ-2
π
J = ∫ x sin xdx ; I = ∫ 2 x 2 cos 2 xdx 2 0
2
2
ﻧﻀﻊ-3
0
J وI ﺛﻢ اﺳﺘﻨﺘﺞI − J وI + J أﺣﺴﺐ
1 1 1 ﺗﺄآﺪ أن/ أ-1 − = t t + 2 t (t + 2) 1 1 t +2−t 1 − = = t t + 2 t (t + 2) t (t + 2) 2
∫1 2
∫1
dt dt t (t + 2)
ﻧﺤﺴﺐ/ب
21 2 1 1 3 dt = ∫ − dt = ln t − ln ( t + 2 ) 1 = ln 2 − ln 4 + ln 3 = ln 1 t t (t + 2) t+2 2
π
A = ∫ 2 e x sin xdx 0
π
ﻧﺤﺴﺐ-2
π
π
π
A = e x sin x 2 − ∫ 2 e x cos xdx = e x sin x 2 − e x cos x 2 − K 0 0 0 0 π
π
1 A = e x sin x 2 − e x cos x 2 0 0 2 π
= ......... π
J = ∫ 2 x sin xdx ; I = ∫ 2 x 2 cos 2 xdx 2
2
0
J +I =∫
π
2 x2 sin 2 0
xdx + ∫
π
2 x2 cos2 0
xdx = ∫
0
π
2 x2 0
( cos
2
)
π
π
1 3 2 2 x2 dx = 3 x 0 0
I − J ﻧﺤﺴﺐ
1
-3
I + J ﻧﺤﺴﺐ
x + sin x dx = ∫ 2
ﻧﻀﻊ
=
π3 24