Chapter 6.5, Problem 18E

dx x² +9 2. Use an appropriate trigonometric substitution to rewrite J as J(a simplified trig function of 0) d0. Carefully show your work with differentials and use of trig identities to help simplify. Then find the integral. Show any use of substitutions and reasoning with right triangles.

1 -dx 2x + 4 Use SUBSTITUTION to evaluate the definite integral to three decimal places. Clearly demonstrate the following steps in order to earn full credit: a) What is "u"? What is "du"? b) Rewrite the integral in terms of u and du. c) Evaluate the integral. d) Evaluate the solution. Round final answer to 3 decimal places.

V4x2 49 dx - Evaluate the integral: x3 (A) Which trig substitution is correct for this integral? 1 x = sec(0) 4 49 sec(e) 4 7 -sin(0) 7 z sec(0) 2 sec(0) (B) Which integral do you obtain after substituting for x? Note: to enter 0, type the word theta. do (C) What is the value of the above integral in terms of 0? + C (D) What is the value of the original integral in terms of x? Note: WAMAP does not recognize the inverse secant (arcsec) function. You will need to use another inverse trig function when you fill in your answer below. + C Question Help: D Video