Problem

For the following exercises, use a calculator to …

05:30

Problem 276 Hard Difficulty

For the following exercises, use a calculator to draw the region, then compute the center of mass $(\overline{x}, \overline{y}) .$ Use symmetry to help locate the center of mass whenever possible.
Region between $y=\sqrt{x}, \quad y=\ln (x), \quad x=1$ and $x=4$

Answer

$(2.21,1.07)$

Related Courses

Calculus 2 / BC

Calculus

Chapter 6

Applications of Integration

Section 6

Moments and Centers of Mass

Discussion

You must be signed in to discuss.

Top Calculus 2 / BC Educators

Watch More Solved Questions in Chapter 6

Problem 254

Problem 255

Problem 256

Problem 257

Problem 258

Problem 259

Problem 260

Problem 261

Problem 262

Problem 263

Problem 264

Problem 265

Problem 266

Problem 267

Problem 268

Problem 269

Problem 270

Problem 271

Problem 272

Problem 273

Problem 274

Problem 275

Problem 276

Problem 277

Problem 278

Problem 279

Problem 280

Problem 281

Problem 282

Problem 283

Problem 284

Problem 285

Problem 286

Problem 287

Problem 288

Problem 289

Problem 290

Problem 291

Problem 292

Problem 293

Problem 294

Video Transcript

Okay, so we're asked to job region. So we have wise equal to the square root of X and Y is equal to island of X, and this is from 1 to 4. So let's see that this is from one before we're gonna have something. See, I believe our reboot of expansion would feel like Bess Intern are Ellen. Function would go like this. So we're looking for this region over here, right? This is a skirt of X, and this is Ellen of X. Okay, So since there's no cemeteries were gonna just calculate our center of mass directly So expert is equal to the interval from what did we say? It was once before, uh, x times our top minus our bottom graph. So that's extensive Root of X, which is extremely over too. Minus x ellen of X e x over Inter Girl from just X 1/2 minus Ellen of x The X once before. So this gives me to over five x 25 over to minus one. Have X squared Ellen of X minus one over four x squared all over to over three extra three over to punish ex Elena X minus X all about what it evaluated up from four. It's one, yet it simplifies to see the Tickle to 3 to 3 over 20 minus eight Owen before over 47 over six. It's what it's for. Ellen of four. Okay, so that's approximately equal to 2.2. And now we have y bar that's equal to 1/2 in your little phone once before. Over top function Square two This is X minus R bottom function, which is owned of X Squared the X all over in a row from what? Four of X 1/2 oneness. Elena vets. Okay, what does that give me that? Give me 1/2 times one. Have X squared minus ex Ellen squared X money to excel in X plus two X All over 47 are actually that's 47 over +61 is for Elena Fort. We don't need to evaluate this from 4 to 1. Okay, this becomes 1/2 3 over 21 is for Ellen, where four plus eight. Evelyn of four over 47. Over six minutes. Four. Ellen before which is approximately 1.7 So our center of rash becomes 2.2 comma. 1.7

We have video lessons for 94.98% of the questions in this textbook