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Unformatted text preview: ) = 1 √ 2+ t 4 , and by FTC1, g ( x ) = F ( x 2 )F (tan x ). Therefore, by chain rule, g ′ ( x ) = F ′ ( x 2 )2 xF ′ (tan x ) sec 2 x = 2 x √ 2 + x 8sec 2 x √ 2 + tan 4 x 3. Evaluate the integral ∫ π/ 4 1 1 + cos 2 θ cos 2 θ dθ. Solution: ∫ π/ 4 1 1 + cos 2 θ cos 2 θ dθ = ∫ π/ 4 1 ( 1 cos 2 θ + 1 ) dθ = ∫ π/ 4 1 ± sec 2 θ + 1 ² dθ = tan θ + θ ] π/ 4 1 = (1 + π/ 4)(tan 1 + 1) = π/ 4tan 1 . 2...
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 Fall '06
 McAdam
 Calculus, Derivative, Riemann integral, Riemann sum, Riemann

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