Solutions Homework 10

# Solutions Homework 10 - MATH 106 CALCULUS I FOR BIO& SOC...

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Unformatted text preview: MATH 106 CALCULUS I FOR BIO. & SOC. SCI. FALL 2011 INSTRUCTOR: JOS ´ E MANUEL G ´ OMEZ Solutions Homework 10. Please show all your work. (1) (6 Points) Find the most general antiderivative of the following functions: (a) (2 Points) f ( x ) = x 3 + 2 x 3 . Solution: The most general antiderivative of f ( x ) is F ( x ) = x 4 4- 1 x 2 + C. (b) (2 Points) g ( x ) = √ x + 3 √ x + 4 √ x . Solution: Note that g ( x ) = x 1 / 2 + x 1 / 3 + x 1 / 4 . Therefore the most general antiderivative of g ( x ) is G ( x ) = 2 x 3 / 2 3 + 3 x 4 / 3 4 + 4 x 5 / 4 5 + C. (c) (2 Points) h ( x ) = sec 2 (2 x ). Solution: The most general antiderivative of h ( x ) is H ( x ) = tan(2 x ) 2 + C. (2) (6 Points) Compute the following integrals: (a) (3 Points) integraldisplay parenleftbigg e − 3 x + 2 x parenrightbigg dx. Solution: integraldisplay parenleftbigg e − 3 x + 2 x parenrightbigg dx =- e − 3 x 3 + 2 ln | x | + C....
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Solutions Homework 10 - MATH 106 CALCULUS I FOR BIO& SOC...

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