Find the volume of the solid obtained when the region under the curve y = arcsin x, x > 0, is rotated about the y-axis.
> Evaluate the integral. |O tan'o do
> Evaluate the integral. | sin 6x cos 3x dx
> Evaluate the integral. sec 0 tan 0 o - J sec'o – sec 0
> Evaluate the integral. /3 sin 0 cot 0 do Jw/6 sec 0
> Evaluate the integral. 1 + sin x dx 1 + cos x
> Evaluate the integral. 12 1 + 4 cot x dx Ja/4 4 - cot x
> Evaluate the integral. |V3 – 2x – x² dx
> Evaluate the integral. 3/3 3 dx 2
> Evaluate the indefinite integral as a power series. What is the radius of convergence? dt
> Evaluate the integral. 1 + x dx
> Evaluate the integral. S,le - 1|dx
> Evaluate the integral. S In(x + vx? – T) dx
> Evaluate the integral. S sin Jat dt
> Evaluate the integral. dx J 1+ e*
> Evaluate the integral. 3x² + 1 dx Jo x³ + x? + x +1
> Evaluate the integral. + tan x)? sec x dx
> Evaluate the integral. + dx
> Evaluate the integral. In x -dx x/1 + (In x)²
> Evaluate the integral. | arctan /x dx
> Find a power series representation for f, and graph f and several partial sums sn(x) on the same screen. What happens as n increases? f(x) = tan (2x)
> (a) Approximate f by a Taylor polynomial with degree n at the number a. (b) Use Taylor’s Inequality to estimate the accuracy of the approximation / when x lies in the given interval. (c) Check your result in part (b) by graphing / S
> Evaluate the integral. t cos?t dt Jo CoS
> Evaluate the integral. x? dx VI - x2
> Evaluate the integral. X sec x tan x dx
> Evaluate the integral. In(1 + x²) dx
> Evaluate the integral. ( sin't cos't dt
> Evaluate the integral. 2х — 3 dx x' + 3x
> Evaluate the integral. 1 dx x'/x² – 1
> Evaluate the integral. cos(1/x) · dx ах
> Evaluate the integral. х+ 2 dx 2 х3 + 3х — 4
> Evaluate the integral. Se sin t cos t dt |t sin t
> Find a power series representation for f, and graph f and several partial sums sn(x) on the same screen. What happens as n increases? 1 + x S(x) = In 1- x
> Evaluate the integral. - dx (2х + 1)°
> Evaluate the integral. dt t* + 2
> Evaluate the integral. sin'x dx cos x
> Evaluate the integral. ( Vỹ In y dy
> Evaluate the integral. (3r + 1)7 dx
> Evaluate the integral. cos x dx 1- sin x
> Computer algebra systems sometimes need a helping hand from human beings. Try to evaluate with a computer algebra system. If it doesn’t return an answer, make a substitution that changes the integral into one that the CAS can evaluate.
> Use a computer algebra system to evaluate the integral. Compare the answer with the result of using tables. If the answers are not the same, show that they are equivalent. dx V1 + x
> Use a computer algebra system to evaluate the integral. Compare the answer with the result of using tables. If the answers are not the same, show that they are equivalent. | tan'x dx
> Find a power series representation for f, and graph f and several partial sums sn(x) on the same screen. What happens as n increases? f(x) = In(1 + x*)
> Use a computer algebra system to evaluate the integral. Compare the answer with the result of using tables. If the answers are not the same, show that they are equivalent. - x² dx
> Use a computer algebra system to evaluate the integral. Compare the answer with the result of using tables. If the answers are not the same, show that they are equivalent. | cos*x dx
> Use a computer algebra system to evaluate the integral. Compare the answer with the result of using tables. If the answers are not the same, show that they are equivalent. dx e*(3e* + 2)
> Use a computer algebra system to evaluate the integral. Compare the answer with the result of using tables. If the answers are not the same, show that they are equivalent. fxVF + 4 dx
> Use a computer algebra system to evaluate the integral. Compare the answer with the result of using tables. If the answers are not the same, show that they are equivalent. Sese'x dx
> Use a computer algebra system to evaluate the integral. Compare the answer with the result of using tables. If the answers are not the same, show that they are equivalent. | sec'x dx
> Verify Formula 53 in the Table of Integrals (a) by differentiation and (b) by using the substitution t = a + bu.
> Find a power series representation for f, and graph f and several partial sums sn(x) on the same screen. What happens as n increases? 2 S(x) – %3D x? + 1
> Use the Table of Integrals on Reference Pages 6–10 to evaluate the integral. sec20 tan´0 do 9 – tan?0
> Use the Table of Integrals on Reference Pages 6–10 to evaluate the integral. x*dx r10 – 2 - 2
> Use the Table of Integrals on Reference Pages 6–10 to evaluate the integral. |e' sin(at – 3) dt
> Use the Table of Integrals on Reference Pages 6–10 to evaluate the integral. 2x – 1 dx
> Use the Table of Integrals on Reference Pages 6–10 to evaluate the integral. dx 2x
> Use the Table of Integrals on Reference Pages 6–10 to evaluate the integral. cos '(x-2)
> Use the Table of Integrals on Reference Pages 6–10 to evaluate the integral. x*e* dx
> Use the Table of Integrals on Reference Pages 6–10 to evaluate the integral. 4 + (In x)² – dx
> Use the Table of Integrals on Reference Pages 6–10 to evaluate the integral. Sx'arcsin(x²) dx
> Use the Table of Integrals on Reference Pages 6–10 to evaluate the integral. ( sec'x dx
> Find a power series representation for the function and determine the radius of convergence. x² + x f(x)- (1 – x)'
> Use the Table of Integrals on Reference Pages 6–10 to evaluate the integral. x'/4x² – xª dx Jo
> Use the Table of Integrals on Reference Pages 6–10 to evaluate the integral. · dx 3 - e2x
> Use the Table of Integrals on Reference Pages 6–10 to evaluate the integral. sin 20 do /5 – sin 0
> Use the Table of Integrals on Reference Pages 6–10 to evaluate the integral. S sin'x cos x In(sin x) dx
> Use the Table of Integrals on Reference Pages 6–10 to evaluate the integral. dx 2x – 3x?
> Use the Table of Integrals on Reference Pages 6–10 to evaluate the integral. S V6 + 4y – 4y² dy
> Use the Table of Integrals on Reference Pages 6–10 to evaluate the integral. dt 21
> Use the Table of Integrals on Reference Pages 6–10 to evaluate the integral. coth(1/y) dy y?
> Use the Table of Integrals on Reference Pages 6–10 to evaluate the integral. x'sinx dx
> Use the Table of Integrals on Reference Pages 6–10 to evaluate the integral. arctan Vr dx
> Find a power series representation for the function and determine the radius of convergence. 1 + x (1 – x)? S(x -
> Use the Table of Integrals on Reference Pages 6–10 to evaluate the integral. fx/2 + x* dx
> Use the Table of Integrals on Reference Pages 6–10 to evaluate the integral. ( cos"0 do
> Use the Table of Integrals on Reference Pages 6–10 to evaluate the integral. /2y² – 3 dy ,2
> Use the Table of Integrals on Reference Pages 6–10 to evaluate the integral. 9x² x? /9х2 + 4 dx
> Use the Table of Integrals on Reference Pages 6–10 to evaluate the integral. w/8 arctan 2x dx
> Use the indicated entry in the Table of Integrals on the Reference Pages to evaluate the integral. tan(Tx/6) dx; entry 69
> Use the indicated entry in the Table of Integrals on the Reference Pages to evaluate the integral. I V - x dx; entry 113
> Use the indicated entry in the Table of Integrals on the Reference Pages to evaluate the integral. w/2 cos 5x cos 2x dx; entry 80
> Show that 1 3 Tn + 2 3 Mn = S2n
> Show that 1 2 (Tn + Mn) = T2n
> Find a power series representation for the function and determine the radius of convergence. 3 f(x) = 2 - x
> Sketch the graph of a continuous function on [0, 2] for which the right endpoint approximation with n = 2 is more accurate than Simpson’s Rule.
> Sketch the graph of a continuous function on [0, 2] for which the Trapezoidal Rule with n = 2 is more accurate than the Midpoint Rule.
> The region bounded by the curve y = 1/(1+e-x) the x- and y-axes, and the line x = 10 is rotated about the x-axis. Use Simpson’s Rule with n = 10 to estimate the volume of the resulting solid.
> The table shows values of a force function f(x), where x is measured in meters and f(x) in newtons. Use Simpson’s Rule to estimate the work done by the force in moving an object a distance of 18 m. 6 9 3 12 15 18 f(x) 9.8 9.1 8.5 8
> Use Simpson’s Rule with n = 8 to estimate the volume of the solid obtained by rotating the region shown in the figure about (a) the x-axis and (b) the y-axis. y. 4 8 10 x 4. 2. 2.
> Shown is the graph of traffic on an Internet service provider’s T1 data line from midnight to 8:00 am. D is the data throughput, measured in megabits per second. Use Simpson’s Rule to estimate the total amount of data
> Find a power series representation for the function and determine the radius of convergence. S(x) · (1 + 4x)?
> The table (supplied by San Diego Gas and Electric) gives the power consumption P in megawatts in San Diego County from midnight to 6:00 am on a day in December. Use Simpson’s Rule to estimate the energy used during that time period. (Us
> Water leaked from a tank at a rate of r(t) liters per hour, where the graph of r is as shown. Use Simpson’s Rule to estimate the total amount of water that leaked out during the first 6 hours. 4 2 0 2 4 6 1 (seconds)
> The graph of the acceleration a(t) of a car measured in ft/s2 is shown. Use Simpson’s Rule to estimate the increase in the velocity of the car during the 6-second time interval. 12 8 4 4 6 t(seconds) 2.
> A radar gun was used to record the speed of a runner during the first 5 seconds of a race (see the table). Use Simpson’s Rule to estimate the distance the runner covered during those 5 seconds. t (s) v (m/s) 1 (s) v (m/
> A graph of the temperature in Boston on August 11, 2013, is shown. Use Simpson’s Rule with n = 12 to estimate the average temperature on that day. TA (F) 80 70 60- noon 4 8 4.
> The widths (in meters) of a kidney-shaped swimming pool were measured at 2-meter intervals as indicated in the figure. Use Simpson’s Rule to estimate the area of the pool. 5.6 5.0 6.8 7.2 4.8 4.8 6.2
> Estimate the area under the graph in the figure by using (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpson’s Rule, each with n = 6. y4 1 1 3 4 5 6 x 2.
> Find the approximations Tn, Mn, and Sn for n = 6 and 12. Then compute the corresponding errors ET, EM, and ES. (Round your answers to six decimal places. You may wish to use the sum command on a computer algebra system.) What observations can you make? I
> Find a power series representation for the function and determine the radius of convergence. f(x) = x² tan '(x')
> Find the approximations Tn, Mn, and Sn for n = 6 and 12. Then compute the corresponding errors ET, EM, and ES. (Round your answers to six decimal places. You may wish to use the sum command on a computer algebra system.) What observations can you make? I
