Assignment 3

# Assignment 3 - your answers. (a) Z ln 3 x x d x (b) R sin 5...

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MAT 1330 3X Assignment 3 Due date: July, 12 Total: 10 points Problem 1. [ 2 points ] (i) For each of the following descriptions write a diﬀerential equation and ﬁnd its solution. (a) Section 4.1, exercise 16 (b) Section 4.1, exercise 17 (ii) Apply Euler’s method with the given value of Δ t to the diﬀerential equation and compare the result with the exact result from the previous problem. (a) Section 4.1, exercise 22 (b) Section 4.1, exercise 23 Problem 2. [ 2 points ] Compute the antiderivatives of the following functions. Check your answers. (a) f ( x ) = x ( x + 1)( x + 2) (b) f ( x ) = x 2 + x + 1 x (c) f ( x ) = ( x + 1)( x - x + 1) (d) f ( x ) = ± 3 x + 1 x 3 x ² 2 1

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Problem 3. [ 2 points ] Use substitution to compute the following indeﬁnite integrals. Check
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Unformatted text preview: your answers. (a) Z ln 3 x x d x (b) R sin 5 x cos x d x (c) Z e tan x cos 2 x d x (d) R e x sin( e x )d x Problem 4. [ 2 points ] Use integration by parts to evaluate the following indenite integrals. Check your answers. (a) R x ln x d x (b) Z x cos 2 x d x (c) Z ln x x 3 d x (d) Z ln( x 2 + 1)d x ( Hint : Use Z 1 x 2 + 1 d x = tan-1 x + C ) Problem 5. [ 2 points ] Compute the following: (a) Z e 1 ln x x d x (b) Z 10 1 x ( 5 x 2-1)d x (c) Z 2 sin 4 x cos x d x (d) Z 2 x cos x d x 2...
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## This note was uploaded on 12/19/2011 for the course MAT 1330 taught by Professor Dumitriscu during the Fall '08 term at University of Ottawa.

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Assignment 3 - your answers. (a) Z ln 3 x x d x (b) R sin 5...

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