# L34 - x-axis and f x = 1 x(ln x 2 from x = e to x = e 2 10...

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L34 – The Substitution Rule Consider Z 6 x 2 (2 x 3 + 1) 5 d x . Substitution Rule – If u = g ( x ) is a diﬀerentiable function whose range is an interval I and f is continuous on I , then Z f ( g ( x )) g 0 ( x ) d x = Z 6 x 2 (2 x 3 + 1) 5 d x = 1

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Z 8 x 2 - 4 2 x 3 - 3 x d x = Z sin(cos( x ))sin( x ) d x = 2
Z e (1+ 1 x ) x 2 d x = Z cos( x ) sin 3 ( x ) d x = 3

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Z (1 + x ) 2 - x d x = 4
Z e 3 x 1 + e x d x = 5

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Z 1 x p ln( x ) d x = 6
Find a formula for Z tan( x ) d x Z cot( x ) d x 7

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Find a formula for Z sec( x ) d x Z csc( x ) d x 8
Substitution Rule for Deﬁnite Integrals – If g 0 ( x ) is continuous on [ a,b ] and f is continuous on the range of g , then Z b a f ( g ( x )) g 0 ( x ) d x = Evaluate Z ln(2) 0 e 3 x d x . 9

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Find the area of the region bounded by the

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Unformatted text preview: x-axis and f ( x ) = 1 x (ln( x )) 2 from x = e to x = e 2 . 10 Evaluate: Z ln(3) ( e x + 1) 2 e x d x 11 Integrals of symmetric functions. Suppose f is continuous on [-a,a ]. a) If f is even, then Z a-a f ( x ) d x = b) If f is odd, then Z a-a f ( x ) d x = 12 Find the area between the x-axis and f ( x ) = x 4-4 x 2 from x =-2 to x = 2. 13 Evaluate: Z 2-2 x p 4-x 2 d x 14...
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L34 - x-axis and f x = 1 x(ln x 2 from x = e to x = e 2 10...

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