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Find the area under the curve $y=\frac{1}{(x+1)^{3 / 2}}$ bounded on the left by $x=3$
Area $=1$
Calculus 1 / AB
Calculus 2 / BC
Chapter 3
Techniques of Integration
Section 7
Improper Integrals
Integration
Integration Techniques
Missouri State University
Oregon State University
University of Michigan - Ann Arbor
University of Nottingham
Lectures
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In mathematics, integratio…
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Evaluate the area under ea…
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So this question were given that Y equals one over X plus one to the power of three over to an X equal street. So now we know that the area on the first quadratic between my taxi street can be given by this interval. So this is our first stop right here. Right in the center. Pull. And now we can write. This is alone, you limit asked. He goes to infinity. I mean, see how the animal we have three. An infinity. But now we're gonna make this with three and t. So three tea substituting tea for infinity. And then we have want over X plus one to the power of three. Over two. Yes. Now we can write this portion of the limit keeping this statement the same we could rewrite. This is negative too. Over the swimmer to box plus one Jeanne, up here. All right, Wilby. And up with you. Evaluate which the limit is. He goes to defend you of one minus two over the square root of T minus one t plus sponsor. So when we evaluate this, where we're gonna end up with is one for the reason that fucking an infinity will give us a very, very large denominator. And that, too over this huge number, your infinite denominator. We'll just be what kind of something inevitable. Which is why this approach is for and this is for the area.
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