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1. Integration by parts (IBP) is a technique that finds the integral of a product of functions in terms of the integral of the product of their derivative and antiderivative. Given a function u = f(x), v = g(x) and their derivatives, what is the correct IBP formula for fudv? a. uv-fvdu b. u-f du c. uv + f udv d. -uv-fvdu 2. Applying IBP, evaluate fx√x + 1dx (x-1)+(x + 1)² + C a. c. (x + 1)² - 4(x + 1)² + c b. (x+1)+(x + 1)² + C d. (x + 1)(x + 1) + C 3 3. What can be used for trigonometric substitution if the integrand contains the form (a²-b²x²) where a and b are constants? a. y = =sin 0 b. y = sec 0 c. y ==tan 0 d. y ==csc 0

1. Integration by parts (IBP) is a technique that finds the integral of a product of functions in terms of the integral of the product of their derivative and antiderivative. Given a function u = f(x), v = g(x) and their derivatives, what is the correct IBP formula for fudv? a. uv-fvdu b. u-f du c. uv + f udv d. -uv-fvdu 2. Applying IBP, evaluate fx√x + 1dx (x-1)+(x + 1)² + C a. c. (x + 1)² - 4(x + 1)² + c b. (x+1)+(x + 1)² + C d. (x + 1)(x + 1) + C 3 3. What can be used for trigonometric substitution if the integrand contains the form (a²-b²x²) where a and b are constants? a. y = =sin 0 b. y = sec 0 c. y ==tan 0 d. y ==csc 0

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Answer the following with the correct letter.  If the answer is not on the choices given, indicate the correct answer. Show formal solution comprehensively and legibly (only applicable to computational items).

1. Integration by parts (IBP) is a technique that finds the integral of a product of functions in terms of the integral of the product of their derivative and antiderivative. Given a function u = f(x), v= g(x) and their derivatives, what is the correct IBP formula for fudv? a. uv-fvdu c. uv + fudv d. -uv-f vdu b. u- f du 2. Applying IBP, evaluate fx√x + 1dx 3 5 a. (x-1)+(x + 1)² + C c. (x + 1)²-(x + 1)² + c 15 15 3 3 b. (x+1)+(x + 1)² + C d. (x + 1)²-(x + 1)² + c 15 3. What can be used for trigonometric substitution if the integrand contains the form C. y = tan 0 d. y ==csc0 (a²-b²x²) where a and b are constants? a. y = =sin 0 b. y = =sec 0
Transcribed Image Text:1. Integration by parts (IBP) is a technique that finds the integral of a product of functions in terms of the integral of the product of their derivative and antiderivative. Given a function u = f(x), v= g(x) and their derivatives, what is the correct IBP formula for fudv? a. uv-fvdu c. uv + fudv d. -uv-f vdu b. u- f du 2. Applying IBP, evaluate fx√x + 1dx 3 5 a. (x-1)+(x + 1)² + C c. (x + 1)²-(x + 1)² + c 15 15 3 3 b. (x+1)+(x + 1)² + C d. (x + 1)²-(x + 1)² + c 15 3. What can be used for trigonometric substitution if the integrand contains the form C. y = tan 0 d. y ==csc0 (a²-b²x²) where a and b are constants? a. y = =sin 0 b. y = =sec 0
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