Find f(x), assuming that f(x) ex dx = f(x) e' - 8x-1 ex dx. (Use C for the constant of integration.) Evaluate the integral. (Use C for the constant of integration.) cos 498(3y) sin?(3y) dy
Question 13 Evaluate XV1 dx. (A) 1/2 (B) 7/4 (C) -1/2 (sin-+ +8?_1-30 vi-x+c (D) (E) None of above. OB OC OD E ОА Question 1 dr (A) X +C Evaluate s - 16 (22+16) Ž V22 +16 -X (B) -1 + c 472 +16 (C) +C 1677 +16 (D) +C 16/22 +16 X A OD ОВ OC
Evaluate the following integral using integration by parts. ( 164 16x In 9x dx Use the integration by parts formula so that the new integral is simpler than the original one. Choose the correct answer below. O A. 8x In (8x?) - S(9x) di O B. 9x In (9x) S(8x2) OC. 8x? In (9x) – (8x) dx D. 8x In (8x) – (9x) dx
hind the derivative. y = 12x dy + 5x + 8x, find dx O A. dy = -24x dx - 3 + 15x2 OB. dy =- - 24x - 1 + 15x² + 8 dx O C. dy dx - 24x - 1 + 15x2 OD. dy dx -3 - - 24x + 15x2 + 8
QUESTION 8 | * 4* dx = O A. x(41) 4* In 4 +C In24 OB. (41) + In4 In24 to OC x2 (4*) 2(In 4) +C 4- OD. x(4+) In4 to In24 O E x 4" - 4* +C
8. Evaluate the indefinite integral: S(5x3 + 2 cos x )dx a. b. S(4x3 – 8x + 7) dx
QUESTION 14 Find the area of the region specified by the integral(s). Sol dxdy+ [*L* dx dx dy OA 32 OB 4 oc 8 OD 128 OE 64
Find the indefinite integral: * dx x-1
Use the following integral. sin(x) dx = sin(x) - x cos(x) + C Find the volume of the solid generated by revolving each plane region about the y-axis. (0) yos (1) y 8 7 6
Evaluate the following integral. x² dx √ 121 + x² What substitution will be the most helpful for evaluating this integral? O A. x= 11 sec 0 O B. x= 11 tano O C. x= 11 sino Find dx. dx = dᎾ Rewrite the given integral using this substitution and simplifying. so x dx - Sodo √121 + x² Evaluate the indefinite integral. x²dx s √121+x² (Use C as the arbitrary constant.)