2­1 M ore Trigonom e tric Inte grals (9971911)
Question
1.
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2
3
4
5
6
7
Question Details
sp16 trig int 1 [3450528]
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sp16 trig int 2 [3450529]
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sp16 trig int 3 [3450530]
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Find the antiderivative following the steps below. Do not use a calculator or other machine
assistance.
sin3 x dx
a. Use the property sin3 x = sin2 x sin x to rewrite this integral.
b. Rewrite the resulting antiderivative using the Pythagorean Identity sin2 x + cos 2 x = 1.
c. Use the substitution u = cos x to rewrite the problem in terms of u and du.
d. The resulting problem is an elementary antiderivative. Find the antiderivative, convert back to the original
variable x, and include +C.
sin3 x dx = 2.
Question Details
Find the antiderivative. Do not use a calculator or other machine assistance.
cos3 x dx = Use the property cos3 x = cos2 x cos x.
3.
Question Details
Find the antiderivative. Do not use a calculator or other machine assistance.
sin5 x dx = 4.
Question Details
sp16 trig int 4 [3450531]
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sp16 trig int 5 [3450998]
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sp16 trig int 6 [3450999]
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sp16 trig int 7 [3451002]
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Find the antiderivative following the steps below. Do not use a calculator or other machine
assistance.
sin(5x) sin(3x) dx
a. Use the Product­to­Sum Identity
sin a sin b = 1
1
cos(a − b) − cos(a + b)
2
2
to rewrite this integral.
b. The resulting problem is an elementary antiderivative. Find the antiderivative and include +C.
sin(5x) sin(3x) dx = 5.
Question Details
Find the antiderivative. Do not use a calculator or other machine assistance.
cos(5x)cos(3x) dx = Use the Product­to­Sum Identity cos a cos b = 6.
1
1
cos(a − b) + cos(a + b).
2
2
Question Details
Find the antiderivative. Do not use a calculator or other machine assistance.
sin(5x)cos(3x) dx = 7.
Question Details
Find the antiderivative. Do not use a calculator or other machine assistance.
1
x2
x2 + 1
dx
Use the substitution x = tan u.
a. Use the substitution facts to rewrite the problem in terms of u and du only. Simplify so that the radical is
elimated and the result is in terms of sin(u) and cos(u). Either the triangle facts or a variant of the
Pythagorean Identity sec 2 u = tan2 u + 1 may be helpful.
b. The resulting problem is an anterivative that should look like an antiderivative from an earlier Trigonometric
Integral problem. Find the antiderivative, convert back to the original variable x, and include +C.
1
x2
x2 + 1
dx = Assignment Details
Name (AID): 2­1 More Trigonometric Integrals (9971911)
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