# An elementary course in the integral calculus by Daniel A Murray

By Daniel A Murray

Initially released in 1898. This quantity from the Cornell collage Library's print collections was once scanned on an APT BookScan and switched over to JPG 2000 structure through Kirtas applied sciences. All titles scanned conceal to hide and pages may possibly comprise marks notations and different marginalia found in the unique quantity.

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**Extra info for An elementary course in the integral calculus**

**Example text**

Performs the sum f+g+h +... >> f+g+h Ans = cos (x) + log (x) + 3 * x ^ 2 - x ^ 3 + 1 f-g Find the difference of f and g (f-g) >> f-g Ans = x cos (x) - x ^ 2 + x ^ 3 + 1 (continued) 45 CHAPTER 2 N NUMBERS, OPERATORS, VARIABLES AND FUNCTIONS f-g-h-... Performs the difference f-g-h-... >> f-g-h Ans = 2 * x - cos (x) - log (x) - x ^ 2 + x ^ 3 + 1 f*g Creates the product of f and g (f * g) >> f * g Ans = (cos (x) + 2 * x ^ 2 - x ^ 3) * (x^2 + x + 1) f*g*h*... Creates the product f * g * h *... >> f * g * h Ans = -(x - log (x)) * (cos (x) + 2 * x ^ 2 - x ^ 3) * (x^2 + x + 1) f/g Performs the ratio between f and g (f/g) >> f/g Ans = (x ^ 2 + x + 1) / (cos (x) + 2 * x ^ 2 - x ^ 3).

You can also use the command radsimp. a. >> simplify (sym (2/sqrt (2))) Ans = 2 ^(1/2) b. >> simplify (sym (3/sqrt (3))) Ans = 3 ^(1/2) c. >> syms a >> simplify (sym (a/sqrt (a))) Ans = a^(1/2) 58 CHAPTER 2 N NUMBERS, OPERATORS, VARIABLES AND FUNCTIONS EXERCISE 2-13 Given the vector variables a = [p,2p,3p,4p,5p] and b = [e, 2e, 3e, 4e, 5e] calculate c = sine(a) + b, d = cosh(a), e = Ln(b), f = c * d, g = c/d, h = d 2. 1008 59 CHAPTER 2 N NUMBERS, OPERATORS, VARIABLES AND FUNCTIONS EXERCISE 2-14 Given the vector of the first 10 natural numbers, find: 1.

Pretty (simple ((3*a+2*a+7*a) /(a^3+a))) 12 -----2 a + 1 c. >> pretty (simple ((1 + 1 /(1+a) /(1+a) ^ 2 + 1 /(1+a) ^ 3))) 2 a + 3 a + 3 -----------3 (a + 1) d. >> pretty (simple ((1 + a / (a + b) + a ^ 2 / (a + b) ^ 2))) 2 2 a + b a ---------- + 1 2 (a + b) EXERCISE 2-11 Perform the following operations with irrational numbers: a. 3 a 2 a 5 a 7 a b. 2 3 2 2 2 c. 4a1/3 - 3b1/3 - 5a1/3 - 2b1/3 + ma1/3 d. 3a 27a e. a 3 a f. a 5 a 56 CHAPTER 2 N NUMBERS, OPERATORS, VARIABLES AND FUNCTIONS a.