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0 [ & €Jlemspoint) Previous Problem 1 the area 8 region Next Problem peeet f() 3 !1 Area 2 Provlew My Aniswdrs 1 Submit Answers 1 6 0 E: 07 Em x] 1...

Question

0 [ & €Jlemspoint) Previous Problem 1 the area 8 region Next Problem peeet f() 3 !1 Area 2 Provlew My Aniswdrs 1 Submit Answers 1 6 0 E: 07 Em x] 1

0 [ & € Jlems point) Previous Problem 1 the area 8 region Next Problem peeet f() 3 ! 1 Area 2 Provlew My Aniswdrs 1 Submit Answers 1 6 0 E: 07 Em x] 1



Answers

solve the given problems. Describe a region for which the area is found by evaluating the integral $\int_{1}^{2}\left(2 x^{2}-x^{3}\right) d x$

We want to draw the region are and express the region with sedimentation. The region in question is bounded by the functions Why equals four minus X squared. Why equals zero where X is between zero and two. First let's draw this region we're gonna graph are two Y curves as well as set our bounds for X as are given in the equations. So we have the region are highlighted in green. It is bounded by the two Y curves and red, zero and four minus X squared as well as zero and two for X. So now that we've drawn out our region are let's express this region with set notation. So with that notation we write our region our as our equals X. Y. For zero. That's an excellent listen to. Why is between zero and four minus X squared. So f of X equals zero G. Of X equals four minus X squared. That means that this is a regular X region. Because our X bounds are simply numbers and ry bounds our functions.

Okay. This question. We have to find out the area between the graph. Why? That is equals. Two FX equals 200. Okay. And the x X is and the X axis over the indicated interval. That is one coma. Six. Okay, so let's draw the graph here. Okay? So why it cost 200? That will be like this. Okay, this is a graph of Y. Close to 100. Okay. And And the X axis, the interval is one and six. Okay, so let's suppose this will be one comma zero, and this is six comma zero. Okay. And we have to find out the area under these graphs. Okay. Called by these graphs so mhm. You can see it is a rectangle. Okay. And director, in the area of a rectangle is the land multiple above it. So this height will be 100. Okay, export the instruction in the question. We have to use geometric formulas. Okay, so this is 100 and this will be six minus one. Okay, so the area will be that is 100 multiplied by six minus one. Okay, uh, it will be 100 this will be six minus one. So it will be 100 dot and five. And that will be 500. Okay. And this is the area, then it will be in Esquire units. Okay, so this will be your final answer. Thank you.

To compute this integral, we substitute E two x power with its first three terms of the serious expansion. And these eco's Ax squared just Eriks killed plus extra fall. So we're too and it's anti derivative. Yes. Once our X cubed plus 1/4 extra fourth plus 1/10 extra faith and 80 girls 581 over Hamburg and 87,000 and five younger. So the value is approximately zero three zero nine 8667.

To compute this integral, we substitute E two x power with its first three terms of the serious expansion. And these eco's Ax squared just Eriks killed plus extra fall. So we're too and it's anti derivative. Yes. Once our X cubed plus 1/4 extra fourth plus 1/10 extra faith and 80 girls 581 over Hamburg and 87,000 and five younger. So the value is approximately zero three zero nine 8667.


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