please help me with this hw , 8.6

Use integral tables to evaluate the integral. I3xw/ 10x - x2 dx Click here to view page 1 of the Table of Integrals. Click here to view page 2 of the Table of Integrals. Click here to view page 3 of the Table of Integrals. Click here to view page 4 of the Table of Integrals. Click here to view page 5 of the Table of Integrals. I3x] 10)()(2 dx = |:| Use integral tables to evaluate the integral. 8 sin 7t sin 2 Click here to view page 1 of the Table of Integrals. Click here to view page 2 of the Table of Integrals. Click here to view page 3 of the Table of Integrals. Click here to view page 4 of the Table of Integrals. Click here to view page 5 of the Table of Integrals. . . . 8 sin 7t sin - dt = NUse a substitution to change the integral into one that can be found in an integral table. Then evaluate t I15 arcsin ,/;dx Click here to view page 1 of the Table of Integrals. Click here to view page 2 of the Table of Integrals. Click here to view page 3 of the Table of Integrals. Click here to view page 4 of the Table of Integrals. Click here to view page 5 of the Table of Integrals. - OO OO OO G J.15 arcsin dx= |:| Use a substitution to change the integral into one that can be found in an integral table. Then evaluate the integral. _[ cot (16t)4/1 - sin 2(16t) dt Click here to view page 1 of the Table of Integrals. Click here to view page 2 of the Table of Integrals. Click here to view page 3 of the Table of Integrals. Click here to view page 4 of the Table of Integrals. Click here to view page 5 of the Table of Integrals. Icot(16t)d1 - sin(16t)dt=| | Use a substitution to change the integral into one that can be found in an integral table. Then evaluate the integral. I cot (8t)4 1 - sin2(8t)dt Click here to view page 1 of the Table of Integrals. Click here to view page 2 of the Table of Integrals. Click here to view page 3 of the Table of Integrals. Click here to view page 4 of the Table of Integrals. Click here to view page 5 of the Table of Integrals. f cot (81)/1 - sin8t)dt=| | Use reduction formulas to evaluate the integral. Ia cot*t dt Click here to view page 1 of the Table of Integrals. Click here to view page 2 of the Table of Integrals. Click here to view page 3 of the Table of Integrals. Click here to view page 4 of the Table of Integrals. Click here to view page 5 of the Table of Integrals. - > J.8c0t4tdt=|:| Use reduction formulas to evaluate the integral. I19x4(|n x)2dx Click here to view page 1 of the Table of Integrals. Click here to view page 2 of the Table of Integrals. Click here to view page 3 of the Table of Integrals. Click here to view page 4 of the Table of Integrals. Click here to view page 5 of the Table of Integrals. - o I19x4(|n x2dx=| | 1 Find the centroid of the region cut from the fourth quadrant by the curve y = - 4/_1 and the line x=8. X+ Click here to view page 1 of the Table of Integrals. Click here to view page 2 of the Table of Integrals. Click here to view page 3 of the Table of Integrals. Click here to view page 4 of the Table of Integrals. Click here to view page 5 of the Table of Integrals. - O -+ The x-coordinate of the center of mass is |:| (Type an exact answer.) The head of your firm's accounting department has asked you to find a formula she can use in a computer program to calculate the year-end inventory of gasoline in the company's tanks. A typical tank is shaped like a right circular cylinder of radius r and length L, mounted horizontally, as shown in the accompanying figure. The data come to the accounting office as depth measurements taken with a vertical measuring stick marked in centimeters. Complete parts (a) and (b). L +Measuring stick r - AT a. Show, in the notation of the figure, that the volume of gasoline that fills the tank to a depth d is V =2L J A r? y2 dy. The bottom of the tank has a y-coordinate of y = -r+d -r What is the largest value the following integral can have for any a and b? Give reasons for your answer. b I/xxz dx a Select the correct choice below and, if necessary, fill in the anser boxes within your choice. (Simplify your answers. Type exact answers, using as needed. Use integers or fractions for any numbers in the expressions.) A. The integrand is both positive and negative, so the integral is maximized by integrating over | | 0, a#1) 6. sin x dx = - cos x + C 7. cos x dx = sin x + C 8. | sec 2 x dx = tan x + C 9. | csc x dx = - cotx + C 10. sec xtan x dx = secx + C 11. csc xcot x dx = - cscx + C 12. tan x dx = In /sec x | + C 13. cotx dx = In | sin x | + C 14 . sinh x dx = coshx + C dx 15. cosh x dx = sinh x + C 16. -= arcsin - + c Na2 -x a dx dx 17. = - arctan - + c 18. a = -arcsec + c a *v x - a a dx 19. = sinh - 1- + c (a>0) dx 20 . = = cosh 1- +c (x> a>0) - a2 a Forms involving ax+b 21. J (ax + b)"dx = (ax + b ) " + 1 -+ C, n# -1 22 . x( ax + b ) " dx = ( ax + b)n * 1 [ax + b a(n + 1) a2 + C, n# -1, -2 n+2 n + 1 23 . J (ax + b ) " ' dx = = In lax + b / + c 24. x ( ax + b) "'dx = - - - In lax + b| +c 25. J x(ax + b)-2dx = - In lax + b/ + + c 26. dx X x(ax + b) - In ax + bl + C 27 . J ( Vax +b ) " dx = 2 (vax+b) " + 2 Vax + b dx n+ 2 -+ C, n# - 2 28 -dx = 2 vax + b + b X Wax + b dx /ax + b - vb 29a dx - In C 29b ax - b Vb - arctan + C x vax + b Wax +b + vb xvax - b b Vax + b Wax + b dx 30. dx Vax + b 2 -+ C 31 . x vax + b x Wax + b bx 2b xvax + b\f9/8/24, 1:48 PM Table of Integrals for trigonometric forms (page 3) Trigonometric Forms 63. sin ax dx = - - cos ax + C 64. cos ax dx = - sin ax + C 65. sin 2ax dx = X sin 2ax +c 4a 66. cos 2ax dx = 2 + sin 2ax + C 4a 67. | sin "ax dx = - sin " ax cos ax " sin "- 2ax dx na 68. | cos "ax dx = Cos " ax sin ax na n- 1 [ cos "-2 ax dx 69a. sin ax cos bx dx = cos (a + b)x cos (a-b)x . a2#b 2 (a + b) 2(a - b) 69b sin ax sin bx dx = sin (a - b)x sin (a +b)x 2(a - b) 2(a + b) - + C, a2 # b2 69c. cos ax cos bx dx = sin (a - b)x sin (a + b)x + C, a2 #b2 2(a - b) 2(a + b) 70. sin ax cos ax dx = _ cos 2ax - + C 4a 71. sin "ax cos ax dx = sin " * ax 72. cos ax (n + 1)a - +C, n# -1 Sin ax dx = = In | sin ax| + C 73. cos "ax sin ax dx = -. cos +1 Tax sin ax (n+ 1)a -+ C, n# - 1 74. cos ax dx = - - In |cos ax | + C 75. sin "ax cos max dx = _ sin " - ax cosm+ 1 a + - n - 1 a(m + n) m +n . sin " -2 ax cos "ax dx, n# - m (reduces sin "ax) 76. sin "ax cos max dy = sin" ax cosm-1, m - 1 a(m + n) sin "ax cosm-2ax dx, m# -n (reduces cos max) dx 77 . - 2 b - c arctan tan b + csin ax avb2 -c2 b +c 4 ax + C . b 2 > c 2 C + b sinax + vc-bcos ax 78. In + C, b2 0 (page 4) Inverse Trigonometric Forms 103. arcsin ax dx = xarcsin ax + = 1-a2x2 + c 104. arccos ax dx = x arccos ax - - 1 -a2x2 + c 105 . arctan ax dx = x arctan ax - 27 In (1+ a2x2) + c 106. x" arcsin ax dx =- n+1 *n+ dx - arcsin ax - , n# -1 n+1 1+1 1 1-ax 107. x" arccos ax dx = *n+1 - arccos ax + - a dx 5: n# -1 n+ 1 n + 1 11-a-x2 108. x" arctan ax dx = = n+1 x dx n + 1 arctan ax - n + 1 1+2,2: 0# - 1 Exponential and Logarithmic Forms 109. Jeax ax = meax + c 110. bax dx = 1 bax a inb + C, b > 0, b# 1 111 . xe * dx = -2 ( ax - 1 ) + C 112. J x"eax dx = 1x"eax _ _ fx"-1eax dx 113. x" bax dx = *" bax alnb " alnbJ x - 1bax dx, b > 0, b# 1 eax 114. eax sin bxdx = -2 , 2 (a sin bx -bcos bx) + C ax 115. eax cos bx dx = a2 + 62 (a cos bx + b sin bx) + C 116. In ax dx = xInax - x + C 117 . x" ( In ax ) m dx = *"* ( In ax)m n + 1 1 + 1 . -x" ( In ax)m - 'dx, n # - 1 118. Jx ' ( In ax)" dx = (In ax) m + 1 m + 1 - +C, m# -1 119. dx x In ax = In |In ax| + c Forms involving 12ax - x", a > 0 120. dx - = arcsin 2ax - x2 ( x -2) + c 121. 2ax - x2 dx = * 2 2ax -x2 + 2 arcsin +C 122. (2ax-x2 ) "dx= (X-a) (