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Find the exact area under the given curves between the indicated values of $x$. The functions are the same as those for which approximate areas were found in Exercises $5-14$.$y=\frac{1}{x^{2}},$ between $x=1$ and $x=5$

Calculus 1 / AB

Chapter 25

Integration

Section 3

The Area Under a Curve

Integrals

Missouri State University

Baylor University

University of Michigan - Ann Arbor

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okay. And this problem? We're trying to find the area contained by the four curves shown in the graph The Blue Line X equals negative to the green line. X equals one. The red curve Y equals two X squared plus five and the X axis where y equals zero. We're gonna set up in a girl, uh, shows this area. The integral will be from negative 2 to 1. And the function that were integrate is two x squared plus five with a lower boundary of zero. The anti derivative of this integral is 2/3 x to the third plus five x. And we're gonna evaluate this from negative 2 to 1. Can we first plug in the upper limit, which is one. And we will then subtract that from the same anti derivative evaluated that negative too. Okay, In the first set, we're gonna get 17 over three subtracted by and in the second set. Cool. Get negative. 46 3rd This gives us 63 over three, which we can simplify to 21. So the area contained by those four turn those four curves is 21

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