Select the correct answer. Evaluate the integral | (ex - e-*) dx OA. 2ex+C OB. ex +C OC. ex-ex+C OD. extex+CSelect the correct answer. Evaluate the integral | 42x 4-xox O A. 16* +C 2 In 4 OB. 42x +C In 4 O C. 4x +C In 4 OD. 4-x In 4\fSelect the correct answer. Evaluate the integral fe esinx + x jax sec x O A. rite asinx + +C 1+e OB. psin + x In x + C O C. a sinx + In x OD. xite ACOSX + +C 1+eSelect the correct answer. Find the derivative of the function f(x) = (x + 2)* using logarithmic differentiation. O A. ( 2 + x ] *[_x +In( 2+ X)] 2+X OB. (2+ X)[ X + In(2 + x )] 2+X O C. X + In(2 + X )] 2+ X OD. (2+X)[(2+x)* +In(2+x)]Select the correct answer. Find the area under the curve 3/ . any? from 1 to 2. A. 0.095 B. 1.008 C. 2.883 D. 5.975 Select the correct answer. Evaluate the integral [sec(3x +1)dx , A. %|n|sec(3x + 1) + {30(3" "' 1)| + C B. 3913866): 4- 1) 4' tan(3x "' 11+ C c. %In|sec 3x + tan3x| * C D. 3 In|sec(3x + 1)tan(3x + 1)| + C Select the correct answer. sec' x [an x Evaluate the integral! o'x A. In |tan x| + C B. In |sec x| + C C. In |x| + C D. In |secxtan x| + C Select the correct answer. An archaeologist finds a barren land with a large number of fossils of Dinosaurs. The number NM of fossils that can be found per cubic meter after tyears can be determined by solving the equation: = 5000 dl 6 5' Assuming that the initial number of fossils is 100. estimate the number of + fossils after 10 years. \" A. 2098.24 " B. 2333.59 " C. 4580.64 " D. 4719.86 Select the correct answer. The population of Brazil was 10.112 million in 1855 and 12.51 million in 1860. Estimate the population of Brazil in 1870. " A. 11.82 million B. 12.81 million " C. 19.15 million " D. 20.00 million irevious-question Ct answer: Hot custard in heated at a temperature of 194F. It is then allowed to cool in the refrigerator at a temperature of 41 \"F. The custard cools to 140F in 20 minutes. What will be the temperature of the custard after 80 minutes? A. 51.33F B. 56.37F C. 65.41F D. 67.82F Select the correct answer. Strontium-90 has a half-life of 28.1 years. How many years will it take for a sample of Strontium-90 to decay to 25% of its initial quantity? " A. 46.7 years " B. 56.2 years C. 67.2 years D. 70.3 years Select the correct answer Determine how long it will take for a principal amount of $1 ,500 to become double its initial value when deposited into an account paying interest at a rate of 13%, continuously compounded. 5.33 years A \" B. 6.32 years C 11.25 years D 14.33 years \fSelect the correct answer. 10 Solve the integral ] dx . tan - (x)( 1+x2 ) O A. sin - ( To ) +C OB. tan -1(1+ x2 )+C OC. 10 sin-1 +C tan( x ) OD. 20vtan -1 x + CSelect the correct answer. Solve the Integral dx . 100 - 8x2 O A. sin 1 1/8x 10 + C OB. V8 sin 18x 10 -+ C O C. V2 tan-1 8x 12 OD. Sec -1 10x 10 + CSelect the correct answer. Find the area under the curve of the function 11 between the limits 0 and 4. x + 16 3 /'_'\\_ B. n ,---\\. C. l 1 5 D. 5 4 Select the correct answer. Evaluate the integral | e * sinh (e* + 5) dx . O A. cosh(5) + cosh(ex) + c O B. cosh(ex + 5) + C O C. 5cosh(ex) + c O D. cosh(5) +ex + C\fSelect the correct answer. Evaluate the integral sech(3x) sinh(3x) dx . cosh(3x) O A. csch(3x)+C OB. - -csch? (3x)+C O C. sech? (3x)+C OD. 1 sech (3x)+CFind the area of the shaded region. 3 2 y = - V1+ 49x2 -2 -1 XN O A. 2.644 O B. 2.732 OC. 0.386 O D. 0.378