Question

Please help me understand these problems.

They already have answer keys; however, it is too short for me to understand.

For Question 10, if you can do all again with clearly steps by steps, it will help me a lot.

For Question 2, I only need to explain how I can sketch the right triangle exactly (2a only). Why that value must on that side? for example: why ”x” must be in adjacent side?

Thank you a lot.

10. Consider the f(x) = 6 tan (). a. When evaluatingf6 tan-1 (E) dx by parts, what are your choices of u and of dv (and what would du and v be?)? y= dy skp. dy dus dy= du pl: as is opthonal b. Evaluate f 6 tan1(E) dxz lo(tai(4 dy -56 3du kip du-2 skp 2. Consider the function h(x) a. Sketch the right triangle that corresponds to evaluating the integral of this function (and label both legs and the hypotenuse as well as 0). b. When integrating g(x)de, i what is your choice of x? i what would dx be? dr- ii what would 0 be? iv. what would x+2 be? dx, c. Find (HintS: Your answers in a and b will help. x2+2=(V2 and tan0+1 see20 will also help.) Clan sev'gedo fsecs

Answer 1

(x) 6 tan Given function is J(x)dx=6 dx tan Let =tan dv dx 1 d du 2 dx3 1 dx dx 2 tan = xtan 1+ - = xtan -1 = xtan +9 X = xtan 3 X 2 (x +9) -1 = xtan In 3 (6+)- 3 /(x)dx= 6 xtan - _- 3 2 -91n (x2 +9) 6xtan