Calc05_3 - 5.3 Definite Integrals and Antiderivatives Use graphs and your knowledge of area and 1 0 x = 4 1 1 1 3 3 0 1 2 2 4 1 3 3(1 0 4 3 3 1 3 13 0 4

Calc05_3 - 5.3 Definite Integrals and Antiderivatives Use...

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5.3 Definite Integrals and Antiderivatives
Use graphs and your knowledge of area and x 3 0 1 δξ = 1 4 το εωαλυατε τηε ιντεγραλ . α 29 ξ 3 -1 1 δξ β 29 ξ 3 + 3 ( 29 0 1 δξ χ 29 ξ -2 ( 29 3 2 3 δξ δ29 ξ 3 -1 1 δξ δ29 1 - ξ 3 ( 29 0 1 δξ ε 29 ξ -1 ( 29 3 -1 2 δξ 0 13 4 1 4 1 2 3 4 - 1 4
Use graphs and your knowledge of area and x 3 0 1 δξ = 1 4 το εωαλυατε τηε ιντεγραλ . γ 29 ξ 2 ÷ 3 0 2 δξ η 29 ξ 3 -8 8 δξ ι 29 ξ 3 -1 ( 29 0 1 δξ ϕ 29 ξ 3 0 1 δξ 0 1 2 - 3 4 3 4
1. ( 29 0 a a f x dx = ò If the upper and lower limits are equal, then the integral is zero. 2. ( 29 ( 29 b a a b f x dx f x dx = - ò ò Reversing the limits changes the sign. ( 29 ( 29 b b a a k f x dx k f x dx × = ò ò 3. Constant multiples can be moved outside. ( 29 ( 29 ( 29 ( 29 b b b a a a f x g x dx f x dx g x dx + = + é ù ë û ò ò ò 4. Integrals can be added and subtracted.

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