We wish to evaluate the indefinite integral I=∫dx(x2−2x+5)32 (a) Show that after an appropriate trigonometric substituti
Posted: Wed Jul 06, 2022 1:21 pm
We wish to evaluate the indefinite integral
I=∫dx(x2−2x+5)32
(a) Show that after an appropriate trigonometric substitution, the integral I can be reduced to
B∫cosφdφ
for some constant B. Clear indicate what the correct constant B is. Hint: first complete the square.
(b) Complete the evaluation of the integral I. Your final answer must be expressed in terms of the variable x, and should not involve any trigonometric or inverse trigonometric functions.
Use proper mathematical notation and show all relevant steps in your solution.
I= = dx 3 (x² - 2x + 5) ² 2 J
Bc cos ydy
I=∫dx(x2−2x+5)32
(a) Show that after an appropriate trigonometric substitution, the integral I can be reduced to
B∫cosφdφ
for some constant B. Clear indicate what the correct constant B is. Hint: first complete the square.
(b) Complete the evaluation of the integral I. Your final answer must be expressed in terms of the variable x, and should not involve any trigonometric or inverse trigonometric functions.
Use proper mathematical notation and show all relevant steps in your solution.
I= = dx 3 (x² - 2x + 5) ² 2 J
Bc cos ydy