A solid lies between planes perpendicular to the x-axis at x= - 4 and x= 4. The cross-sections perpendicular to the x-axis between these planes are squares whose bases run from the semicircle y = - v16 -x to the semicircle y = v16 - x . Find the volume of the solid. The volume of the solid is cubic units. (Simplify your answer.)Find the volume of the solid generated by revolving the shaded region about the The volume of the solid is | cubic units. X-axis. (Type an exact answer, using it as needed.) O 3x + 4y = 12 in-Find the volume of the solid generated by revolving The region bounded by y = 4x2, y = l], and x = 3 about the xaxis. The volume of the solid generated by revolving the region bounded by y = 103, 5!: U, and x: 3 about the xaxis is I: cubic units. (Type an exact answer, using \"II as needed.) 1: 51: Find the volume of the solid generated by revolving the region bounded by 3: 31,1' sin x, 51: [Land x1 = 3 and x2 = ? about the xaxis. I 5: The volume of the solid generated by revolving the region bounded by v = SJsin x, v = [Land x1 = and x2 = about the )Haxis is :l cubic units. 3 6 (Round to the nearest hundredth.) Find lhe volume of the solid generated by revolving The region bounded by The given curve and lines about the yaxis. 5 1i?\" <:> x= ,x=D,y=D,y='i V: (Type an exact answer, using 11: as needed.) Find the volume of the eolid generated by revolving the region bounded by the given curve and lines about the xaxis. y=4x, y=4, x= v=n (Type an exact answer, using 11: as needed.) Find the volume ofthe solid generated by revolving the following region about the given axis. The region in the rst quadrant bounded above by the curve y =x2. below by the xaxis, and on the right by the line x=1, about the line x: 2_ V : (Type an exact answer, using 1: as needed.) Use the shell method to find the volume of the solid generated by revolving the shaded region about the x-axis. V3 y = V5 . X The volume is (Type an exact answer, using it as needed.) Use The shell method to nd the volume eflhe solid generated by revolving the shaded region about the yaxis. y a la. The volume is |:. (Type an exact answer, using 11: as needed.) Find the volume of the solid generated by revolving the region bounded by v: 4x x2 and y = it about the yaxis and about the line x = 3. What is the volume of the solid generated by revolving the region bounded by v = 4x x2 and y = it about the yaxis? Volume = Cl (Type an exact answer, using 11: as needed.) What is the volume of the solid generated by revolving the region bounded by v = 4x x2 and y = it about the line 3: = 3'? Volume = Cl (Type an exact answer, using 11: as needed.) Find the length of the following curve. If you have a grapher, you may want to graph the curve to see what it looks like. y = ( x 2 + 1 ) 3/2 WIN from x = 3 to x = 9 The length of the curve is (Type an exact answer, using radicals as needed.)7 Find the length of the curve x = + 42 on 3 Ey $ 5. 2y 7 The length of the curve x = = 42 2y on 3 sys 5 is (Type an integer or a fraction, or round to the nearest tenth.)Find the length of the curve x = w w 4y from y = 1 to y = 3. The length of the curve is. (Type an integer or a simplified fraction.)\fCheck whether each of the following functions is a solution of the differential equation 3y' + 7y =4e -X (a) y=ex (b)yzexte - (7/3)x (c)y=e* + Ce - (7/3)x (a) Find 3y', 7y, and 3y' + 7y for y = e -X. 3y'= 7y = 3y'+ 7y= Is the function y =e * * a solution of 3y' + 7y =4e -*? Choose the correct answer below. O Yes O No (b) Find 3y', 7y, and 3y' + 7y for y =e -X + e -(7/3)x 3y' = 7y = 3y' + 7y =Check whether each of the following functions is a solution of the differential equation 3y' + 7y =4e -X. (a) y=e - x (b)y=exte - (7/3)x (c)y=ex + Ce - (7/3)x 3y' + 7y = Is the function y =e -* + e -/3) a solution of 3y' + 7y =4e -*? Choose the correct answer below. O No O Yes (c) Find 3y', 7y, and 3y' + 7y for y= e "* + Ce - (7/3)x 3y' = 7y = 3y' + 7y = Is the function y=e "* + Ce -(73)X a solution of 3y' + 7y =4e -*? Choose the correct answer below. O Yes O No\fThe half-life of polonium is 139 days, but your sample will not be useful to you after 82% of the radioactive nuclei present on the day the sample arrives has disintegrated. For about how many days after the sample arrives will you be able to use the polonium? The polonium sample can be used for approximately | days. (Round to one decimal place as needed.)The instructions for the given integral have two parts, one for the trapezoidal rule and one for Simpson's rule. Complete the following parts. - (4x2 + 7) dx I. Using the trapezoidal rule a. Estimate the integral with n = 4 steps and find an upper bound for ET T = (Type an exact answer. Type an integer or a simplified fraction.) An upper bound for | ET| is (Round to two decimal places as needed.) b. Evaluate the integral directly and find | ET. (4x2 + 7) dx = [ - 1 (Type an exact answer. Type an integer or a simplified fraction.)The instructions for the given integral have two parts, one for the trapezoidal rule and one for Simpson's rule. Complete the following parts. [ (4x 2 + 7) dx - 1 c. Use the formula ( ET /(true value)) x 100 to express ET | as a percentage of the integral's true value. % (Round to the nearest integer as needed.) Il. Using Simpson's rule a. Estimate the integral with n = 4 steps and find an upper bound for | Es). (Type an exact answer. Type an integer or a simplified fraction.) An upper bound for |Es | is b. Evaluate the integral directly and find | Es|. 1 ( 48 2 + 7 ) Ox = - 1 (Type an exact answer. Type an integer or a simplified fraction.)The instructions for the given integral have two parts, one for the trapezoidal rule and one for Simpson's rule. Complete the following parts. (4x2 + 7) dx a. Estimate the integral with n = 4 steps and find an upper bound for Es S =0 (Type an exact answer. Type an integer or a simplified fraction.) An upper bound for |Es | is b. Evaluate the integral directly and find | Es). 1 ( 4X 2 + 7 ) dx = 1 - 1 (Type an exact answer. Type an integer or a simplified fraction.) Es| = c. Use the formula ( Es /(true value)) x 100 to express Es as a percentage of the integral's true value. % (Round to the nearest integer as needed.)A rectangular swimming pool is 38 ft wide by T5 it long. The table gives depths {d} from x = E] at the shallow end to the diving end. Use the Trapezoidal Rule with ?5 n = 15 to estimate the volume of the pool, U = I38 - d()() dx. 0 U 511] 15 2D 25 31] 35 41] 45 51] 5551] 55m T5 5 7.2 3.2 3.9 9.5 1D 1U.51U.911.311.?12.112.412.713.113413J The volume of the pool is 113. (Round to the nearest integer as needed.)