CHOOSE ANSWERS FROM THE OPTIONS A TO D.

Question 1 O Mark this question Find the following indefinite integral: (487/ x2 + 23- 21 + X dx O 144 5 - * '+ 23x - 21 In |x | - 5 +c 144 w / en O 5 X + 23x - 21 In |x | - - 5 O 80x 3 + 23x - 21 In |x | + 25 In|x| + c 144 w / C O 5 x 3 + 23x - 21 In|x| + 25 In|x| +cQuestion 2 O Mark this question Find the average value and the value(s) of c guaranteed by the mean value theorem for integrals if f(x) = x-+3 over the interval [0,3]. O favg = 6 O favg = 18 6=./ 15 O favg = 18 6= -/ 15 and c = 1 15 Ofavg= 6 c= - /3 and c =1/3Question 3 O Mark this question Find the following indefinite integral: 12x9- 15x3 + 27x4 dx 3x5 O 4 5 +9 In x +c 6 27 1 O .X -10 X + -10 6 27 O 5 3 X NU X + X +c 5 4x 4 O 5 -5x+ 9 In x +cQuestion 4 O Mark this question Use a Riemann sum with 6 rectangles of equal width to approximate the area between f(x) = x-+ 1 and the x-axis on the interval [1,4]. Use the right-hand endpoint of each subinterval. O 27.875 units O 16.5 units O 20.375 units- O 8.25 unitsQuestion 5 O Mark this question Solve y' = 18x-+ 12ex-9, given that the solution passes through the point (1, - 3). O y= 6x3 _2e - bx+6 - 9x + 2 O y= 6x3 -2e - 6x +6 - 7 O y= 6x3+2ex+6- 11 O y= 6x3+ 2e -6x+6-9x - 2Question 6 O Mark this question Find the indefinite integral: 12x 3 cos( x4 + 27)dx O 3sin(x* + 27) +c O - 3sin(x* + 27) +c 3x4 sin x5+ 27x+c O - 3x sin -x3+ 27x +c\fQuestion 9 O Mark this question 3 Evaluate 7xdx using the fundamental theorem of calculus. 2 O 7x'dx =2315 -2 o 7xdx = 4655 2 O 7x'dx = - 2315 - 2 3 O 7x dx = - 4655 2Question 10 O Mark this question Use the table of integration formulas to identify and use an appropriate formula to find the following definite integral: 28 tan-(7x) dx 4- TI O 28 - 4+ TI O 28 1 - TI O - 1+ 1 O 7Question 11 O Mark this question Find the following indefinite integral: 1 (150 * + + + 3sinx )dx O 15e*+4 In|x| -3cosx + C O 15e* + + 3cosx + c X O 15e* + 4 In|x| + 3cosx+ c O 15ext -3cosx + c XQuestion 12 O Mark this question Evaluate the following definite integral: 1 (20 5 x + 1 - x 3 ) dx O J (20 5 x + 1 - x 3 ) dx = =e' + ON 4 e O J (20 5x +1 - x 3)dx = - ON + OIIN e A O ( 2 0 5 x + 1 - x 3 ) dx = e 4 e O (20 5x+ 1 - x 3 ) dx = e 4Question 13 O Mark this question Approximate the area of the region bounded by y = - x +9, the x-axis, x = - 4, and x =0 by finding the combined area of the rectangles (as shown in each figure) and averaging the results. (0, 9) -10 (0, 9) (-2, 8) (-2, 8) (-4, 5) (-4, 5) O 12.5 units O 9 units O 22 units O 30 units2