2/27/2014
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HW 6.2 PART-1 (5477622)
Question
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Description
SP2013: 2(C); F2012: 2(B); SP2011: 3 (E), (F); F2010: 2(C); SP2009: 2(E);
1.
Question Details
SEssC alc2 6.2.001.MI. [2560568]
-
SEssC alc2 6.2.009. [2165767]
-
SEssC alc2 6.2.016. [2560230]
-
Evaluate the integral. (Use C for the constant of integration.)
4 sin2 x cos3 x dx
Solution or Explanation
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2.
Question Details
Evaluate the integral.
π/2
0
5 sin2x cos2x dx
Solution or Explanation
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3.
Question Details
Evaluate the integral. (Use C for the constant of integration.)
9 cos2x sin 2x dx
Solution or Explanation
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4.
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Question Details
SEssC alc2 6.2.003. [2165799]
-
Evaluate the integral.
π/2
0
sin5 θ cos5 θ dθ
Solution or Explanation
The symbols
and
indicate the use of the substitutions {u = sin θ, du = cos θ dθ} and {u = cos θ, du = −sin θ dθ},
respectively.
π/2
0
sin5 θ cos5 θ dθ =
π/2
0
0
=
5.
1
sin5 θ cos4 θ cos θ dθ =
u5(1 − u2)2 du =
1 6
1
1 10
u − u8 +
u
6
4
10
1
0
1
π/2
0
sin5 θ(1 − sin2 θ)2 cos θ dθ
u5(1 − 2u2 + u4) du =
=
0
1
1
1
−
+
6
4
10
−0 =
1
0
(u5 − 2u7 + u9) du
10 − 15 + 6
1
=
60
60
Question Details
SEssC alc2 6.2.013. [2560223]
-
Evaluate the integral. (Remember to use ln |u| where appropriate. Use C for the constant of integration.)
7 cos2x tan3x dx
Solution or Explanation
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6.
Question Details
SEssC alc2 6.2.017. [2559988]
-
Evaluate the integral. (Use C for the constant of integration.)
2 tan x sec 3 x dx
Solution or Explanation
2 tan x sec 3 x dx =
=
2 tan x sec x sec 2 x dx =
2u2 du
[u = sec x, du = sec x tan x dx]
2 3
2
u +C =
sec 3 x + C
3
3
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7.
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Question Details
SEssC alc2 6.2.019. [2559982]
-
SEssC alc2 6.2.020. [2560232]
-
SEssC alc2 6.2.021. [2560199]
-
Evaluate the integral. (Use C for the constant of integration.)
8 tan2x dx
Solution or Explanation
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8.
Question Details
Evaluate the integral. (Use C for the constant of integration.)
5 tan2x + tan4x dx
Solution or Explanation
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9.
Question Details
Evaluate the integral. (Use C for the constant of integration.)
13 tan4 x sec 6 x dx
Solution or Explanation
Let u = tan x. Then du = sec 2 x dx, so
13 tan4 x sec 6 x dx = 13
= 13
= 13
10.
tan4 x sec 4 x(sec 2 x dx) = 13
u4(1 + u2)2 du = 13
tan4 x(1 + tan2 x)2(sec 2 x dx)
(u8 + 2u6 + u4) du
1 9
2
1
13
26
13
u + u7 + u5 + C =
tan9 x +
tan7 x +
tan5 x + C.
9
7
5
9
7
5
Question Details
SEssC alc2 6.2.022. [2165656]
-
Evaluate the integral.
π/4
0
6 sec 4θ tan4θ dθ
Solution or Explanation
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11.
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Question Details
SEssC alc2 6.2.023. [2166092]
-
SEssC alc2 6.2.025. [2560486]
-
SEssC alc2 6.2.028. [2560036]
-
Evaluate the integral.
π/3
0
5 tan5x sec 4x dx
Solution or Explanation
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12.
Question Details
Evaluate the integral. (Use C for the constant of integration.)
2 tan3x sec x dx
Solution or Explanation
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13.
Question Details
Evaluate the integral. (Remember to use ln |u| where appropriate. Use C for the constant of integration.)
9 tan2x sec x dx
Solution or Explanation
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14.
Question Details
SEssC alc2 6.2.029. [2165526]
-
Evaluate the integral.
π/2
π/6
2 cot 2x dx
Solution or Explanation
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15.
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Question Details
SEssC alc2 6.2.032. [2560423]
-
SEssC alc2 6.2.033. [2560798]
-
Evaluate the integral. (Use C for the constant of integration.)
8 csc 4x cot 6x dx
Solution or Explanation
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16.
Question Details
Evaluate the integral. (Remember to use ln |u| where appropriate. Use C for the constant of integration.)
4 csc x dx
Solution or Explanation
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17.
Question Details
SEssC alc2 6.2.034. [2560366]
-
SEssC alc2 6.2.030. [2165066]
-
Evaluate the integral. (Use C for the constant of integration.)
3 1 − tan2x
dx
sec 2x
Solution or Explanation
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18.
Question Details
Evaluate the integral.
π/2
π/4
cot 3x dx
Solution or Explanation
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19.
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SEssC alc2 6.2.036. [2560833]
-
Evaluate the integral. (Use C for the constant of integration.)
dx
cos x − 1
Solution or Explanation
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Assignment Details
Name (AID): HW 6.2 PART-1 (5477622)
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