1. Given: the ellipse with equation 4x2 9y2 36 Use methods of calculus to find each of the follow...
Calculus (a) Use a substitution to find the indefinite integral | (cosh^{2(x – 1)} Vcosh”[2(x – 1)} – 1) dr where r21. Show your workings. (b) Hence, calculate the definite integral ſi" (cosh" {2(x – 1)} Vcosh?{2(x – 1)} – 1) dar. Give your answer to 2 decimal places.
Directions: Use the graph to find approximate x-coordinates of the points of intersection of the given curves. Then find (approximately- three decimal places) the area of the region bounded by the curves. Also, make a rough sketch of the region sought. You must write the definite integral using proper notation to receive full credit 1) y = χ sin(x*) , y = x6 Directions: Use the graph to find approximate x-coordinates of the points of intersection of the given curves....
Need ONLY 2-3 with work shown Directions: In each problem (1)-(5), write a definite integral of a single variable. For problems marked [FTC], use the Fundamental Theorem of Calculus to evaluate the definite integral. Use a calculator utility for problems marked [Calculator Active]. Show intermediate steps, and box in your final result. « Submit a single team set of solutions on the answer sheets provided.» > (0) Region R is bounded by the curve y -x and the line y...
Use the rectangles to approximate the area of the region. f(x) = -x + 11 [1, 11] y 10 8 6 2 2 4 6 8 10 10 Х Give the exact area obtained using a definite integral. 10 x Need Help? Read it Watch It Talk to a Tutor Use the rectangles to approximate the area of the region. (Round your answer to three decimal places.) f(x) = 25 – x2, (-5,5) y 23 20 15 10 -6 2...
A GRAPHING CALCULATOR IS REQUIRED FOR THIS QUESTION. You are permitted to use your calculator to solve an equation, find the derivative of a function at a point, or calculate the value of a definite integral. However, you must clearly indicate the setup of your question, namely the equation, function, or integral you are using. If you use other built-in features or programs, you must show the mathematical steps necessary to produce your results. Your work must be expressed in...
For the function, do the following. FX) 2 from 1 to b-4. by calculating a Riemann sum using 10 rectangles. Use the method described in Example 1 on page 351, rounding to three (a) Approximate the area under the curve from a to decimal places. square units (b) Find the exact area under the curve from a to b by evaluating an appropriate definite integral using the fundamental Theorem. square units
thats all no more information. 36. Question Details LarCalc11 10.R.065 My No The rectangular coordinates of a point are given. Plot the point -1,2) -42 -2 -2 Find two sets of polar coordinates for the point for 0 smaller 8-value r, 6)- larger 9 value)- θく2 (Round your answers to three decimal places.) 37. Question Details LaiCalc11 10.R 107 МУ Notes Use a graphing utility to graph the polar equation. common intariar of r - 4 -2 sin( and4+2 sin(0)...
HICULTUULUULULUI 2 Task 2 - Trapezium Rule (Maximum Mark 10) Find the equation of the line through the points 1 - ...) a | and B(x) and find an expression for the area under this line between the points A and B. Explain carefully how your result can be used to prove the general formula for the Trapezium Rule. Notes: . This part of the assignment is testing that you can find the equation of a line and use this...
Use the given data set to answer parts (a) and (b). a. Find the regression equation for the data points. b. Graph the regression equation and the data points. x 5 y -2 3 1 3-2 4 4 2 6 a. Find the regression equation for the data points. (Use integers or decimals for any numbers in the expression. Round to two decimal places as needed.) b. Graph the regression equation and the data points. OA. 50 O c. 10...
Task 2 - Trapezium Rule (Maximum Mark 10) Find the equation of the line through the points A(Y) and (.ya) and find an expression for the area under this line between the points A and B. Explain carefully how your result can be used to prove the general formula for the Trapezium Rule. Notes: • This part of the assignment is testing that you can find the equation of a line and use this to derive other formulae. Marking Criteria...