Trigonometric_Integrals.ppt

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SEC 8.2 TRIGONOMETRIC INTEGRALS
Example
Find
Example
Find
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TRIGONOMETRIC INTEGRALS
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1
2
2
to express the remaining factors in terms of cos
to express the remaining factors in terms of sin
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TRIGONOMETRIC INTEGRALS
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sometimes helpful to use
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TRIGONOMETRIC INTEGRALS
Eliminating Square Roots
we use the identity
to eliminate a square root.
Example
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TRIGONOMETRIC INTEGRALS
We can use a similar strategy to evaluate
integrals of the form
Example
Find
Example
Find
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TRIGONOMETRIC INTEGRALS
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1
2
2
to express the remaining factors in terms of sec
to express the remaining factors in terms of tan
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EXAM-2 Term-082
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TRIGONOMETRIC INTEGRALS
the guidelines are not as clear-cut. We may need
to use identities, integration by parts, and
occasionally a little ingenuity.
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TRIGONOMETRIC INTEGRALS
the guidelines are not as clear-cut. We may need
to use identities, integration by parts, and
occasionally a little ingenuity.
Example
If an even power of tangent appears with an odd
power of secant, it is helpful to express the
integrand completely in terms of sec x
Find
Powers of sec x may require integration by
parts, as shown in the following example.
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TRIGONOMETRIC INTEGRALS
Example
Find
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TRIGONOMETRIC INTEGRALS
REMARK
Integrals of the form can be found by similar
methods because of the identity
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1
1
2
2
to express the remaining factors in terms of csc
to express the remaining factors in terms of cot
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EXAM-2 Term-122
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Product of Sines and Cosines
EXAM-2 Term-122
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TRIGONOMETRIC INTEGRALS
Powers of Sines and Cosines
Products of Sines and Cosines
TRIGONOMETRIC INTEGRALS
Powers of tan x and sec x
Eliminating Square Roots
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EXAM-2 Term-092
EXAM-2 Term-092
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TRIGONOMETRIC INTEGRALS
function of Sines and Cosines
function of tan and sec
TRIGONOMETRIC INTEGRALS
function of cot and csc
EXAM-2 Term-092
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EXAM-2 Term-092
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EXAM-2 Term-092
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EXAM-2 Term-092
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