according to me question A(iii) is not correct
Question 2 (Learning Outcome 2) 0 S (*x+3) dx S A) Evaluate the following integrals. 4x+7...
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...
2- Evaluate the following integral: 0.4 | Vcos(2x)dx a) By calculator, b) Composite trapezoidal rule (with segment no. n=4) and determine the true relative error, c) Composite Simpson's 1/3 with n =4 and determine the true relative error, d) Simpson's 3/8 rule determine the true relative error, e) Composite Simpson's rule, with n =5, determine the true relative error.
Question 5. Find the following indefinite integrals: 1. fre'de 4. .Js 3.f x In x dx 6.[(x+5) Ževæ#5dx 2. f x sin 8x dx -5 (1 + In x) sin(x Inx) dx Sin2x sin x cos x dx 5. 7. 5 2x(x2 + 4)5dx 8. dx
Evaluate the following integrals. S 5x-2 dx x2-4 s 9x+25 (x+3)2 dx 2 x3+3x2-4x-12 dx x2+x-6
Z=61 Task 3: Answer the following: a. Evaluate: Siz cos(x) sin?(x) dx (10 Marks) b. The moment of inertia, I, of a rod of mass 'm' and length 4r is given by Ar (2mx? dx where 'x' is the distance from an axis of rotation. Find I. (5 Marks) 2r Task 4: Answer the following: Using the Trapezoidal rule, find the approximate the area bounded by the curve y = ze), the x-axis and coordinates x = 0, x =...
Question 8 a) Find: (3x3 – 5x2 + x - 4) dx (4 marks) b) Use the trapezium rule with 6 strips to approximate the area bounded by the curve y = (x - 1, the x -axis and the lines x = 2 and x = 5 (6 marks)
Q.1 A. Compute each of the following integrals. 0 s V7(5x+3)+ te dv.(2 Marks) (1) Sax 24.dx. (3 Marks) B. (1) Evaluate dx. (3 Marks) (ii) Find the volume generated by revolving the curve y = sin x and y = 0 in 0 SXS ,about the x-axis.(2 Marks)
All of 10 questions, please. 1. Find and classify all the critical points of the function. f(x,y) - x2(y - 2) - y2 » 2. Evaluate the integral. 3. Determine the volume of the solid that is inside the cylinder x2 + y2- 16 below z-2x2 + 2y2 and above the xy - plane. 4. Determine the surface area of the portion of 2x + 3y + 6z - 9 that is in the 1st octant. » 5. Evaluate JSxz...
I. [15 marks] Apply ST/2(0, π/2) and ST/4(0, π/2) to sin x dx, 0 where Sh(a, b) is Simpson's rule applied to the interval [a, b] with hb a. Use s,/2 (0, π/2) and Sn4 (0, π/2) to compute an error estimate for STT/4 (0,7/2). Comment on the quality of the error estimate. I. [15 marks] Apply ST/2(0, π/2) and ST/4(0, π/2) to sin x dx, 0 where Sh(a, b) is Simpson's rule applied to the interval [a, b] with...
4. Consider using the Simpson's 1/3 rule to estimate the following integral I[cos(x 3)l dx (a) Find the approximate values of 1 when the step size h-: 2 and h 1 , respectively. (b) Find an upper bound of the step size h in order to guarantee that the absolute error (in absolute value) of the estimate is less than 0.001. Hint: 2 sin x cos x = sin (2x). I cos x I " The arguments of all trigonometric...