xi = a + idelta x Question 3 Use the following definition to evaluate the integral....
Use the form of the definition of the integral given in the theorem to evaluate the integral. | Previous Answers SCalcET8 5.2.026. Ask Your Teacher 6. 2/4 points My Notes (a) Find an approximation to the integral (x24x) dx using a Riemann sum with right endpoints andn 8. R8 -10.5 n lim> 'f(x;) Ax, where Ax = -and x a + i Ax. Use this to evaluate (b) If f is integrable on [a, b], then f(x) dx (x2-4x) dx...
10) Use Theorem 4 to evaluate. n(n+1) 2 (=1 i = 10 pts 21-11 = n) 2,12 = n(n+1)(2n+1) E=1 43 = {*+1), 2 4 Theorem Iff is integrable on (a, b), then (x) dx = lim 8(xAx where and X; - a +i Ax (2x + 3 (2x + 5)dx
1. Use the definition of integral to show that if f : B → R and f are integrable, then Inf e f 2. Find the volume of the region K between ~ = x2 + 9y2 and z = 18-x2-9y2 (Use Fubini's Theorem) 3. Evaluate Jryz where S is the upper half of the unit sphere. (Use Change of Variable Theorem)
11. (4pts) Use the LIMIT DEFINITION of the integral to evaluate the following integrals. No Credit will be awarded for solutions obtained by using the Fundamental Theorem of Calculus. [ (2-x²)dx
Evaluate each integral using the definition of the definite integral with right endpoints and taking the limit. (Note: You need to write out the Riemann sum and use the summation formulas.) (a) 0 (x^2+2x-5) dx x+b-a/n= xi=a+Ix= (b) 1 x^3 dx x=b-a/n= xi=a+Ix= We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
4.Use Green's Theorem to evaluate the line integral. ∫C 2xydx + (x + y)dy C: boundary of the region lying between the graphs of y = 0 and y = 1 - x2_______ 5.Use Green's Theorem to evaluate the line integral. ∫C ex cos(2y) dx - 2ex sin(2y) dy C: x2 + y2 = a2 _______
A. Express the limit as a definite integral on the given interval. B. Use the form of the definition of the integral to evaluate the integral. n Š lim n-> Xi Ax, [1, 3] (xi +13 * 2 i=1 3 6 (2x - x2) dx
If f is integrable on [a, b], the following equation is correct. Integral^b_a f (x) dx = lim_n rightarrow infinity Sigma^n _i = 1 f (x_i) Delta x, where Delta x = b - a/n and X_i = a + i delta x. Use the given form of the definition to evaluate the integral. integral^1_0 (2 - x^2) dx
No 13 and 14 (a) Find an approximation to the integral [** (x2 - 4x) dx using a Riemann sum with night endpoints and n = 8. Rg (b) iffis integrable on [a, b], then Serum f(x) dx lim 10 Fx) Ax, where Ax Als and Ax. Use this to evaluate 4x) dx
hint This exercise 5 to use the definition of Riemann integral F. Let f : [a, b] → R be a bounded function. Suppose there exist a sequence of partitions {Pk} of [a, b] such that lim (U(Pk, f) – L (Pk,f)) = 0. k20 Show that f is Riemann integrable and that Så f = lim (U(P«, f)) = lim (L (Pk,f)). k- k0 1,0 < x <1 - Suppose f : [-1, 1] → R is defined as...