8 Ay 10- Compute the following estimate of f(x) dx using 0 8- y = f(x)...
8 AY 10- Compute the following estimate of Sf(x) dx using 8- y=f(x) the graph in the figure. 6- T(4) 4- 2- X 0 0 2 4 6 00- 10 Using the Trapezoidal Rule, T(4) = (Type an integer or a simplified fraction.)
Find the solution of the following initial value problem. y'' (t) = 6te! y(0) = 3, y'(0) = 1 y(t) = Let R be the region bounded by the following curves. Use the shell method to find the volume of the solid generated when Ris revolved about the x-axis. y = 21 - x, y=x, and y = 0 Set up the integral that gives the volume of the solid. Use increasing limits of integration. Select the correct choice below...
10. Trapezoidal Rule is used to approximate the integral f(a) dx using 1- (yo +2y1 + 2y2 + x-na b-a + 2yn-1 +%),where Use this approximation technique to estimate the area under the curve y = sinx over。 a. π with n 4 partitions. x A 0 B: @ Δy B-A b. The error formula for the trapezoidal rule is RSL (12ba)1 where cischosen on the interval [a, b] to maximize lf" (c)l. Use this to compute the error bound...
Given the following table of data: 0.00 0.250.500.751.00 f(x) 0.39890.38670.35210.30110.2420 Estimate f(x) dx Estimate Jo f (Q) dx (i) by composite trapezoidal rule (ii) by Romberg integration of 0(h6), R33 Given the following table of data: 0.00 0.250.500.751.00 f(x) 0.39890.38670.35210.30110.2420 Estimate f(x) dx Estimate Jo f (Q) dx (i) by composite trapezoidal rule (ii) by Romberg integration of 0(h6), R33
Evaluate the integral [~ /36+? Sx 736+X?dx=0 Find the area of the region enclosed by the curves y=x2 - 4x and y= -x2 + 4x The area of the region enclosed by the curves is (Type an integer or a simplified fraction.) Use l'Hôpital's rule to find the following limit. 10 In (x-9) x 10+ - (4-10_16->) - ] (ype an integer or lim- (Type an integer or a simplified fraction.) x - 10 In (x-9) X10+
Ay A point P(x,y) is shown on the unit circle corresponding to a real number t. Find the 20 21 values of the trigonometric functions att. The point P is 29 29 O 0 (1.0) sint=(Type an integer or a simplified fraction) COS (Type an integer or a simplified fraction.) Tant-Type an integer or a simplified fraction.) sct (Type an integer or a simplified fraction.) ect Type an integer or a simplified fraction) Type an integer or a simplified fraction)...
The left, right, Trapezoidal, and Midpoint Rule approximations were used to estimate f(x) dx, where f is the function whose graph is shown below. The estimates were 0.7811 0.8675, 0.8632, and 0.9540, and the same number of subintervals were used in each case. (a) Which rule produced which estimate? ?1. Trapezoidal Rule estimate 2. Right-hand estimate 3. Left-hand estimate N4. Midpoint Rule estimate (b) Between which two approximations does the true value of o fa) dx lie? A. 0.8675 β...
Find f(x) dx for each graph of y=f(x), where f(x) consists of line segments and circular arcs. 10 1010 10 HERE AIAH 21 RETH 2 NIE OHHH 0 2 4 6 8 ot 0 10 2 4 6 8 10 a. [) dx = 0 (Type an exact answer, using a as needed.) be prove dx = 0 (Type an exact answer, using a as needed.)
womplete) Find f(x) dx for each graph of y=f(x), where f(x) consists of line segments and circular arcs. O. NO 0 0 2 4 6 8 10 0 2 4 6 8 10 a. Jf(x) dx = 0 (Type an exact answer, using as needed.)
(a) Estimate So sin(x + 1) dx by using either Simpson's Rule or Trapezoidal Rule with n= 6 (Round the answer to 6 decimal places). (b) Estimate the minimum number of subintervals needed to approximate the integrals with an error of magnitude less than 10-4 by the rule you used in part (a).