5. Prove that rb b² – a² xdx = = 2 (Hint: Evaluate the corresponding limit...
(a) Write s} (x2 – 3x)dx as a limit of a Riemann sums. (b) Evaluate this limit exactly using sum properties: n(n+1) and n(n + 1)(2n + 1) 6 2 (c) Use the Fundamental Theorem of Calculus to confirm the result in (b)
2. Express 5* cos adx as the limit of a Riemann sum, using righthand endpoints. Do not evaluate. Final answer:
evaluate the integrals
4. I secer x tan xdx (Hint: Let u = sec x.
Evaluate the limit by first recognizing the sum as a Riemann sum for a function defined on [0, 1]. lim n→∞ n 6i3 5n4 i = 1
(j) ſte tanº e de Hint: Etan2 e. Bonus Questions 1. (2 points) Evaluate the definite integral 2-2 dx as a limit of Riemann sums. Hint: take the sample points x* = Xi-1Xi, i = 1, 2, ..., n. The idea behind partial fractions might also prove helpful. 2. (3 points) Develop a technique of integration using the Quotient Rule (in the same way that the Chair Rule was used to develop the Substitution Rule and the Product Rule was...
Express the integral as a limit of Riemann sums. Do not evaluate
the limit. (Use the right endpoints of each subinterval as your
sample points.)
6
x
1 + x4
dx
4
lim n →
∞
n
i = 1
arctan(36)−arctan(16)2
❌
Express the integral as a limit of Riemann sums. Do not evaluate the limit. (Use the right endpoints of each subinterval as your sample points.) to it yox arctan(36) - arctan (16) Need Help? Read Watch Master It...
Math 378-001 Page 4 Exam 3 10, Evaluate the integralSx I)dx by seting up and computing t the limit of a sum (your choice). Use partitions with n equal subintervals. ion. In particular your solution must include Show all work used to obtain your solut a) formula for the size of subintervals; b) formula for the endpoints; c) the function evaluated at the endpoints or the sup or inf on subintervals; d) the Riemann sum; e simplification and the limit...
3) Evaluate the integral ſx cos xdx using the a) Trapezoidal rule and b) Simpson's rule. For each of the numerical estimates, determine the percent relative true errors.
Express the definite integral as a limit of Riemann sums. DO NOT
EVALUATE.
k (x² + 2 ) dx
(1) Evaluate the following limit using l’Hospital's rule. (Hint: Implicit differentiation and properties of logarithms] -2/3 lim m (+) -