that f'(2) is continuous and that F(x) is an antiderivative of f(1). the following table of...
Problem 5 (7 point) Suppose that f'(x) is continuous and that F(x) is an antiderivative of f(x). You are given the following table of values: r=0 2 = 2 * = 4 x = 6 -2 6 f(x) 6 F(x) 7 2 -4 -3 2 -4 5 3 (a) Evaluate | ((z) – 3)s -3)?f'(x)dx. (b) Evaluate (* 25 r* f" ()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. 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.
e2 3 does not have a complex antiderivative on CV 3. (a) The continuous function f(z) = 0 (b) The continuous function g(z) does not have a complex antiderivative on C 1 + 1리- e2 3 does not have a complex antiderivative on CV 3. (a) The continuous function f(z) = 0 (b) The continuous function g(z) does not have a complex antiderivative on C 1 + 1리-
help 1) 2) 3) Find an antiderivative F(x) of f(x) = 1 + 14x5. F(x) = x + xx6 Substitute appropriately from step 2 to write the summation with index j = 1. 35 35 4 35 7j + 32) = 7 ju 35 4 35 Il j = 1 3 j = 1 Calculate the L, approximation for f(x) cos?(x) on (55 N-1 The formula for left-endpoint approximation is in = Ax f(a + jAx). J = 0 JT...
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...
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
2. Find the intervals on which the following function is continuous. tan r B( ) = V4-12 3. Find the derivatives of the following functions (a) f(z)= /5x +1 (b) gla) = (2r -3)(a2 +2) (c) y = In (x + Vx2 - 1) 4. Find the intervals on which the following function is decreasing. f(z) = 36x +3r2 - 2r 5. Evaluate the following integrals. r dr (a) sec2 tan (b) dar 3 (c) da 5x+1 1. Sketch the...
4. The function f is continuous on the closed interval (-2, 1). Some values of f are shown in the table below. --2 f(x) -3 -1 0 1 7 k3 The equation f(x) = 3 must have at least two solutions in the interval [-1,1) if k = a. 1 b. C. 2 CONN NICO d. 5. If k(r) is a continuous function over the interval (-2, 4) such that k(-2) = 3 and k(4) = 1, then k(2) 0...
If Si f(x)da = 12 and so f(x) = 2.8, find si f(x)dx. Question 2 1 pts Let f(x)dx = 6, S. 8(x)dx = -4, S g(x)da = 12, g(x)dx = 9 Use these values to evaluate the given definite integral: (+1) da