Problem 5 (7 point) Suppose that f'(x) is continuous and that F(x) is an antiderivative of...
that f'(2) is continuous and that F(x) is an antiderivative of f(1). the following table of values: 6 f(x) F() r=0 = 2 r = 4 1 = 6 -2 1 -4 6 2. -3 5 6 -4 2 3 7 (a) Evaluate [u(z) – f(x) – 3)?f'(x)da. b) Evaluate ſz, za f'(x)dx
3) Suppose F(x) is an antiderivative of f(x). Use the graph of the functionf(x) below to answer the following: flx) a) Approximate f'(6), and explain/show how you arrived at your answer 6 4 3 2 b) Explain/show why F'(6) 2 1 2 3 4 5 6 7 c) Approximate o f(x)dx, and explain/show how you arrived at your answer. d) Explain/show why f'(x)dx-3.
(1 point) Let [ f(z)dx=-13, 5° f(x) dx = 3, $*g(x) dx = 6, §*9(a) dx = 1, J2 Use these values to evaluate the given definite integrals. a) ["{$(2) + 9()) dx = 6 .) – g(x)) dx = * (31(2) + 29(2) de = (af(x) + g()) dc = 0. d) Find the value a such that a=
Supposef is continuous on the closed interval [a, b]. if F(x) is an antiderivative of f(x) for all real numbers a,b and k, then the definite integral S* (R8) + k]dx is equal to (A F(b) - F(a) + b-a B F(b) - F(a) +k(b-a) C F(b + k) - F(a + k)+k k F(b)-k F(a) + b-a
3. Consider the following piecewise function (a) Draw an accurate graph of f(). (b) As always, f(x), has an infinite number of antiderivatives. Consider an antiderivative F(r). Let us assume that F(r) is continuous (we don't usually have to specify this, but you will see in the bonus part of the question why we do in this case). Let us further assume that F(2) 1. Sketch an accurate graph of F(r). MATH 1203 Assignment #7-Integration Methods Due: Thurs., Apr. 4...
Problem 4. (6 pts) (a) Suppose that f(x) is a continuous function on 2,7], positive on (2,5) and negative on (5, 7). « [ r(a) dr = 11 and ſsaw) dr = 3, then ind ſis(2) dr. .10 f(x) (b) Suppose that is an even and integrable function. If "L" 3, . f(x) da = 5, then find L" (a) dr.
Question 49 Solve the problem. Suppose that s* r«x) dx = 3. Find f(x) dx = 3. Find S* fix) dx and sfx) dx . 2 0; -3 4; 3 0; 3 3; -3 Question 50 Evaluate the integral. filt-far 0 등 O 626 0%
14. Cousider the following fiunction y()graphed on the interval (0, 10]. The graph between z = 5 and z = 7 is a semicircle having radius 1. (4,0) 2.2) 7,2) 10,0) -2 -f(a) Find the following values. (a) f24/5 f(x) do 23/5 12 (c) g f(x) dx= The area of a circle is πγ2.) (Hint: (d) f(x) dx 10 (e) Suppose that F(x) is the antiderivative of f(x), and assume that F(0) = What is F(2)? What is F(23/5)? F(2)...
1) Given a continuous function g satisfying 90(9)ds = 33 and fo(9)ds = 31. Compute 5 g(s) ds. 2) Determine the general antiderivative for the following function valid for all X+0. (Use C as your arbitrary constant). f(x) = 3 Evaluate the following indefinite integral. Use C for your arbitrary constant. 4) Evaluate the following indefinite integral. Use C as your arbitrary constant. Sæ4e3% dx
1. Calculate the definite integral 1 (229-33 +5) de (a) Find an antiderivative F(x)= (b) Evaluate F(2) F(2) = (c) Evaluate F(1) F(1) = (d) Calculate the definite integral 3x + 5) dx = 2. Calculate the definite integral. Give exact answers. Зе -Te du (a) Find an antiderivative F(*) = (b) Evaluate F(0) F(0) (c) Evaluate F(-1) F(-1) = (d) Calculate the definite integral.