Chap5_Sec4

Chap5_Sec4 - INDEFINITE INTEGRALS Example 1 (5.4) Find the...

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INDEFINITE INTEGRALS Find the general indefinite integral (10 x 4 – 2 sec 2 x ) dx s Using the Table of Indefinite Integral, we have: (10 x 4 – 2 sec 2 x ) dx = 10 x 4 dx – 2 sec 2 x dx = 10( x 5 /5) – 2 tan x + C = 2 x 5 – 2 tan x + C s You should check this answer by differentiating it. Example 1 (5.4)

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INDEFINITE INTEGRALS Evaluate s This indefinite integral isn’t immediately apparent in the Table. s So, we use trigonometric identities to rewrite the function before integrating: Example 2 (5.4) 2 cos 1 cos sin sin sin csc cot csc d d d C θ θ θ  =   = = - + 2 cos sin d
INDEFINITE INTEGRALS Evaluate s Using FTC2 and the Table, we have: Example 3 (5.4) 3 3 0 ( 6 ) x x dx - ( ) ( ) 3 4 2 3 3 0 0 4 2 4 2 1 1 4 4 81 4 ( 6 ) 6 4 2 3 3 3 0 3 0 27 0 0 6.75 x x x x dx - = - = - ⋅ - - ⋅ = - - + = -

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INDEFINITE INTEGRALS Find and interpret the result in terms of areas. The FTC2 gives:
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This note was uploaded on 05/23/2011 for the course MAC 2311 taught by Professor Noohi during the Fall '08 term at FSU.

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Chap5_Sec4 - INDEFINITE INTEGRALS Example 1 (5.4) Find the...

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