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SEC 8.2: TRIGONOMETRIC INTEGRALS

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Presentation on theme: "SEC 8.2: TRIGONOMETRIC INTEGRALS"— Presentation transcript:

1 SEC 8.2: TRIGONOMETRIC INTEGRALS
Example Find Example Find

2 1 1 2 2 TRIGONOMETRIC INTEGRALS
to express the remaining factors in terms of cos to express the remaining factors in terms of sin

3 TRIGONOMETRIC INTEGRALS
1 2 sometimes helpful to use

4 Find Eliminating Square Roots TRIGONOMETRIC INTEGRALS
we use the identity to eliminate a square root. Example Find

5 Find Find TRIGONOMETRIC INTEGRALS
We can use a similar strategy to evaluate integrals of the form Example Find Example Find

6 1 1 2 2 TRIGONOMETRIC INTEGRALS
to express the remaining factors in terms of sec to express the remaining factors in terms of tan

7 EXAM-2 Term-082

8 TRIGONOMETRIC INTEGRALS
the guidelines are not as clear-cut. We may need to use identities, integration by parts, and occasionally a little ingenuity.

9 Find 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.

10 TRIGONOMETRIC INTEGRALS
Example Find

11 REMARK TRIGONOMETRIC INTEGRALS Integrals of the form
can be found by similar methods because of the identity

12 1 1 2 2 to express the remaining factors in terms of csc
to express the remaining factors in terms of cot

13 EXAM-2 Term-122

14 Product of Sines and Cosines
EXAM-2 Term-122

15 Powers of tan x and sec x Eliminating Square Roots
TRIGONOMETRIC INTEGRALS Powers of Sines and Cosines Products of Sines and Cosines TRIGONOMETRIC INTEGRALS Powers of tan x and sec x Eliminating Square Roots

16 EXAM-2 Term-092 EXAM-2 Term-092

17 TRIGONOMETRIC INTEGRALS
function of tan and sec function of Sines and Cosines TRIGONOMETRIC INTEGRALS function of cot and csc EXAM-2 Term-092

18 EXAM-2 Term-092

19 EXAM-2 Term-092

20 EXAM-2 Term-092

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