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You will integrate the following rational function: 20x+5 da S (x-7)(x²-4x+8) To do this, start by writing. 20x+5 (x-7)(x2-4x+8) (a) Put the right-hand side over a common denominator. Enter the numerator of the result. constants: A x-7 (b) Expand the numerator. It is a quadratic in a, which must equal the numerator of the original function. By equating the coefficients you should be able to formulate linear equation in A, B and C. In each case give an equation with the constant part on the right, for example A+ 2 * B = 3. What equation can you deduce from the coefficients of : (d) The last term is in the form Br+C r2-4x+8 + Bx+C x2-4x+8 (c) Solve these three equations, and enter the solution in the form A,B,C Find constants K and J such that B+C = K (2x-4) + J, enter in the form K, J

You will integrate the following rational function: 20x+5 da S (x-7)(x²-4x+8) To do this, start by writing. 20x+5 (x-7)(x2-4x+8) (a) Put the right-hand side over a common denominator. Enter the numerator of the result. constants: A x-7 (b) Expand the numerator. It is a quadratic in a, which must equal the numerator of the original function. By equating the coefficients you should be able to formulate linear equation in A, B and C. In each case give an equation with the constant part on the right, for example A+ 2 * B = 3. What equation can you deduce from the coefficients of : (d) The last term is in the form Br+C r2-4x+8 + Bx+C x2-4x+8 (c) Solve these three equations, and enter the solution in the form A,B,C Find constants K and J such that B+C = K (2x-4) + J, enter in the form K, J

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section: Chapter Questions
Problem 7DE
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You will integrate the following rational function: 20x+5 1₂ dx (x-7)(x²-4x+8) To do this, start by writing 20x+5 (x-7)(x²-4x+8) (a) Put the right-hand side over a common denominator. Enter the numerator of the result. constants: = (d) The last term is in the form x-7 (b) Expand the numerator. It is a quadratic in , which must equal the numerator of the original function. By equating the coefficients you should be able to formulate linear equation in A, B and C. In each case give an equation with the constant part on the right, for example A+ 2 * B = 3. What equation can you deduce from the coefficients of : 22: Bx+C r2-4x+8 Bx+C 2-4x+8 + (c) Solve these three equations, and enter the solution in the form A,B,C Find constants K and J such that B x + C = K (2x-4) + J, enter in the form K, J
Transcribed Image Text:You will integrate the following rational function: 20x+5 1₂ dx (x-7)(x²-4x+8) To do this, start by writing 20x+5 (x-7)(x²-4x+8) (a) Put the right-hand side over a common denominator. Enter the numerator of the result. constants: = (d) The last term is in the form x-7 (b) Expand the numerator. It is a quadratic in , which must equal the numerator of the original function. By equating the coefficients you should be able to formulate linear equation in A, B and C. In each case give an equation with the constant part on the right, for example A+ 2 * B = 3. What equation can you deduce from the coefficients of : 22: Bx+C r2-4x+8 Bx+C 2-4x+8 + (c) Solve these three equations, and enter the solution in the form A,B,C Find constants K and J such that B x + C = K (2x-4) + J, enter in the form K, J
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(e) Separating out the K and J terms, you now have a term of the form and bottom by a constant you should be able to express this in the form (f) Your rational function is now in the form A 2-7 + K(2x-4) x2-4x+8 Don't forget that the integral of 1/x is In (x), not just In (x). B + J 2-4x+8 L c-r)² $2 L 82 By completing the square in the denominator and possibly dividing top for some constants L, r, s, with s> 0. Enter these in the form L, r, s +1 now evaluate the integral. Use a constant of integration F.
Transcribed Image Text:(e) Separating out the K and J terms, you now have a term of the form and bottom by a constant you should be able to express this in the form (f) Your rational function is now in the form A 2-7 + K(2x-4) x2-4x+8 Don't forget that the integral of 1/x is In (x), not just In (x). B + J 2-4x+8 L c-r)² $2 L 82 By completing the square in the denominator and possibly dividing top for some constants L, r, s, with s> 0. Enter these in the form L, r, s +1 now evaluate the integral. Use a constant of integration F.
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