Problem 6. ( 25 points) Let \(a, b\) be positive constants with \(a<b\). Evaluate the integral
$$ \int_{0}^{1} \frac{x^{b}-x^{a}}{\ln x} d x $$
by converting the integral into an iterated double integral and evaluating the iterated integral by changing the order of integration.
Thanks In evaluating a double integral over a region D, a sum of iterated integrals was obtained as follows: 0 f(x, y)dy dr f (r, y)dy d f(x, y) dA -2 2 TJ= Sketch the region and express the double integral integration as an iterated integral with reversed order of
set up iterated integrals for both orders of integration. then evaluate the double integral using the easier order and explain why it's easier. D y dA, D is bounded by y = x - 2, x=y2 (the D next to the double integral should be under the integral. I don't know how to put it in the right spot.
Set up iterated integrals for both orders of integration. Then evaluate the double integral using the easier order. ∫∫DydA, D is bounded by y = x -30; x = y2
Evaluate the given double integral by changing it to an iterated integral. xy dA; S is the triangular region with vertices (0,0), (10,0), and (0,7) O 35 12 0 1225 6 245 12 175 6
The graph of f is shown. Evaluate each integral by interpreting it in terms of areas.(a) \(\int_{0}^{10} f(x) d x\)(b) \(\int_{0}^{25} f(x) d x\)(c) \(\int_{25}^{35} f(x) d x\)(d) \(\int_{0}^{45} f(x) d x\)
for the iterated integral sin(x^2) rewrite the integral reversing the order of integration and evaluate the new integral
10. Consider the integral (x + y + z) dV where D is the volume inside the sphere x2 + y2 + x2 = 9 and above the plane z = 1. (a) (3 marks) Express I as an iterated integral using Cartesian coordinates with the order of integration z, x and y. DO NOT EVALUATE THIS INTEGRAL. (b) (3 marks) Express I as an iterated integral using spherical coordinates with the order of integration p, 0, and 0. DO...
Evaluate the integral 1 ET sin(2²) dx dy by reversing the order of integration. With order reversed, 6 sin(x²) dy dx, where a = ,b= C= and d Evaluating the integral, So S, sin(x2) dx dy =
Problem 5 [10 points] Set up integrals for both orders of integration. Use the more convenient order to evaluate the integral over the plane region R: A R region bounded by y 0, y x, x 4 R 1+x2 a) [2 points] First order b) [2 points] Second order c) [6 points] Evaluate the integral using the more convenient order Problem 5 [10 points] Set up integrals for both orders of integration. Use the more convenient order to evaluate the...
15. (15 points. (a) Sketch the region of integration for the iterated integral . Lzi?dz dy. (b) Evaluate the above iterated integral by reversing the order of integration.