Suppose that f(1) = 1, f(4) = 5, f '(1) = 4, f '(4) = 5, and f '' is continuous. Find the value of
4 | xf ''(x) dx |
1 |
.
Suppose f is continuous, f(0)=0, f(2)=2, f'(x)>0 and f (x) dx = 1. Find the value of the integral fro f-?(x) dx =?
If f is continuous and 6". 16 f(x) dx = 12, find Lox xf(x2) dx.
Suppose f is a continuous function with f(-2) =4 and f(5) = -1. Use a substitution to find 5 ſ e3f(a). f'(x) da -2 to the nearest hundredth.
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
Section 1 — Integration basics and integration techniques 1. Suppose that f(x) and g(x) are continuous functions defined for 0 < x < 4 and that [ f(x) dx = 4 ["f(x) dx = -8 [9(x) dx = 5 ["g(x) dx = -2 Please be extra careful of the bounds in the integrals above. No partial credit will be given. In problems (a-h), either write down the value of the integral, or, write ? if there is not enough information...
ame f(x) If f(x) is a differentiable function, find an expression for the derivative of y= X Choose the correct answer below dy 7f(x)-xf'(x) O A. dx 8 X xf (x) 7f(x) dy O B. dx 8 X dy xf(x) 7f(x) O C. dx 8 X 7f'(x) xf(x) dy O D. dx 8 X
ame f(x) If f(x) is a differentiable function, find an expression for the derivative of y= X Choose the correct answer below dy 7f(x)-xf'(x) O A....
Suppose that f(x) is a continuous function on (2,7), positive on (2,5) and negative on (5,7) If f(x) dx = 3, then find If(x) dar. () dx = 11 and Ś "S" ) dr = = -3, Ls =) dr = 5, (b) Suppose that f is an even and integrable function. If then find Lºs(z) dr.
(2x - 1 if x < -1 2. Suppose f(x) = 2x2 - 4 if-1<x52 (log: (x - 1) if x > 2 a) Is f continuous at x = -1? Justify your answer completely. b) Is f continuous at x = 22 Justify your answer completely. 3. Suppose f(x) = x2 + 3x a) Using the definition of derivative, find f'(x). No credit will be given if shortcuts are used. b) Find the equation of the tangent line to...
Suppose that the functions f and a and their derivatives with respect to a have the following values at the given values of d. Find the derivative with respect to a of the given combination at the given value of 3 x. f(g(x)) =) X=4 xf(x) gla) |f' (a) glo) +433
(4) (12 points) Given the following values of f(x), use integration by parts to evaluate Put the numerical value in an answer box. xf"(x) dx. 2 f(0) 1'0 0 1 2 3 4 5 4 5 3 -2 17 -3 3 0 -5 23