Calculus

# Calculus - Chapter 5 Applications of the Definite Integral...

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Chapter 5 Applications of the Definite Integral 153 Chapter 5 Section 5.1 5. 3 2 , 1, 1 3 y x y x x = = ( ) 3 3 2 1 3 4 3 1 1 4 3 81 27 1 1 3 1 4 3 4 3 160 12 40 3 x x dx x x x = + = + + = = 7. , 1, 2 0 x y e y x x = = 0 2 0 2 2 2 2 ( 1) 2 4 (1 0 0) 2 2 5 x x e x dx x e x e e = + = + = 9. 2 1, 1 , 0 2 y x y x x = = ( ) ( ) ( ) 1 2 2 2 0 1 1 2 2 2 0 1 1 2 2 3 3 2 0 1 1 1 1 (1 ) 2 2 2 2 2 3 3 2 1 1 8 4 1 1 2 (0 0 0) 4 2 2 3 3 2 3 2 3 x x dx x x dx x x dx x x dx x x x x x x + = + + = + + = + + + = 11. 3 1, 1 , 2 2 y x y x x = = ( ) 1 2 3 3 2 1 1 2 2 4 4 2 2 1 1 1 1 (1 ) 2 2 2 4 4 2 1 1 1 1 2 ( 4 2 4) (4 4 2) 2 2 4 4 2 29 2 x x dx x x dx x x x x x x + = + + = − − + + + =

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Chapter 5 Applications of the Definite Integral 155 ( ) ( ) ( ) ( ) 3 3 3 2 0 0 3 3 3 2 3 3 3 3 3 3 3 3 (0 0) 2 3 3 3 3 (9 9) 3 3 3 2 3 x x dx x x x dx x § · = ¨ ¸ © ¹ = = § · = ¨ ¸ © ¹ = = ³ ³ 37.

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