Review for Test 2
Review for Test 2
Review for Test 2
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Solve the initial value problem.<br />
106) dy<br />
dx = 18(6x - 5) -6, y(0) = 1<br />
107) dy<br />
dx = x 4(x5 - 1) 5 , y(1) = 5<br />
Evaluate the integral.<br />
108) ∫ x2(x3 - 6)4 dx<br />
109) ∫ x2<br />
x3 + 3 dx<br />
110)<br />
∫<br />
dx<br />
xln x6<br />
111) ∫ 10x2<br />
4<br />
8 + 2x 3 dx<br />
112) ∫ sin (9x - 2) dx<br />
Use the substitution <strong>for</strong>mula to evaluate the integral.<br />
1<br />
113) x + 1 dx<br />
∫<br />
0<br />
Find the area of the shaded region.<br />
114) f(x) = x3 + x2 - 6x<br />
30<br />
y<br />
25<br />
20<br />
15<br />
(3, 18)<br />
10<br />
5<br />
(0, 0)<br />
-5 -4 -3 -2 -1 -5<br />
1 2 3 4 5<br />
-10<br />
-15<br />
-20<br />
(-4, -24)<br />
-25<br />
-30<br />
x<br />
g(x) = 6x<br />
Find the area enclosed by the given curves.<br />
115) y = 2x - x2, y = 2x - 4<br />
116) y = x3, y = 4x
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