Integrate without table of integration.
1. Sketch the region R of integration. Switch the order of integration and then integrate the problem. π x y cos x dy dx 0 0 2, Find the mass, the moments about the x- and y-axis, and the center of mass of the lamina bounded by the graphs of the given equations. Show a sketch of the region sensie Inx - dydx x
2. Sketch the region of integration for SL to dz dy de and rewrite in the order dy dz dx.
Integrate counterclockwise or as indicated. Show the details. cosh dz, C the boundary of the 2-Ti square with vertices +2, 2, ±4i.
Integrate using basic integration techniques
Integration by substitution 1. Find each of the following indefinite integrals using integration by substitution: dz (a) / (xºcos(x4) ) do (c) / (sin(2) cromka) die (e) / (24) do (a) / (2.eller) die (0) / (zlog.cz) Integration by parts 2. Find each of the following indefinite integrals using integration by parts: (a) / (+cos(x)) dx (c) / (vVy + 1) dy (e) / (sin”(w) ) at (8) / (sin(o) cos(0) ) da (b) / (x2=+) di (a) / (x2108_(2))...
Evaluate the integral $ 3z + 4)cos z dz, C:12+2i = 1 counterclockwise. z² +4 Integrate $c +436 yosz dz, C:/z+3–2i = 3 counterclockwise. (z +4)
Integrate each function without using the table. a) ſcosx In(sinx) dx b) si V x² -16 •doc +2
Triple Integration Problems. 1. Integrate zdV JJ w where ll' is enclosed by the planes z = 0 and cylinders x2 + y2 4 and x2 + y,: 9 = x+9+ 3 and by the 2. Integrate where E is bounded by the zu-plane and the hemispheres z/9-2y2 and z = V/10-22-27 Change the order of integration and evaluate x3 sin(уз)dydx. 0 Jr2 1. Integrate zdV JJ w where ll' is enclosed by the planes z = 0 and cylinders...
Q3. Sketch the region of integration for the integral [5(8,19,2) dr dz dy. (2, y, z) do dzdy. Write the five other iterated integrals that are equal to the given iterated integral. Q4. Use cylindrical coordinates and integration (where appropriate) to complete the following prob- lems. You must show the work needed to set up the integral: sketch the regions, give projections, etc. Simply writing out the iterated integrals will result in no credit. frs:52 (a) Sketch the solid given...
1. Use integration by parts to evaluate the integral: ∫ 6z cos(5z) dz Use integration by parts to evaluate the definite integral. 5t2 In tdt Use integration by parts to evaluate the definite integral: 5se3ds J0.2 Preview Report answer accurate to 3 decimal places. A particle that moves along a straight line has velocity v(t)e3 meters per second after t seconds. How many meters will it travel during the first t seconds (from time-0 to time-t)? 2-3t Evaluate the indefinite...