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Explore Film & Video All About Video Download. Ulead Video Studio 11 Free Download Full Version For Windows [32bit & 64bit] Bit FileHippo.Q:

Find the limit of $\int \sin(x)e^{ -x}\,dx$

I would like to know how to solve the following:
Find the limit of $$\int\sin(x)e^{ -x}dx$$
As far as I know, one should solve this problem by setting $u=\sin(x)$, then one should get $du=-\cos(x)\,dx$, then it becomes $$\int\frac{du}{\cos(x)}$$ where the integral is $\tan(x)$, then it becomes $$x-\tan(x)$$ but I don’t know how to find the limit here because of the minus sign.

A:

The limits of integration need to be established. Start by splitting the integral into two pieces:
$$\int_0^\frac{\pi}4\sin(x)\ e^{ -x}\,dx+\int_{\frac{\pi}4}^\frac{\pi}2\sin(x)\ e^{ -x}\,dx$$
The second half is clearly zero. For the first half, you need to determine the limits of integration. Notice that the derivative of $\sin(x)$ satisfies
$$\sin'(x)=-\cos(x)\qquad\text{and}\qquad \cos'(x)=\sin(x)$$
Since $\sin(x)$ goes through $-1$ at $x=\frac{\pi}4$, the definite integral is equal to
$$\int_0^\frac{\pi}4\ \sin(x)\ e^{ -x}\,dx=-

https://colab.research.google.com/drive/1-vnVPjgS5VvqjuV7iP7J4a_NCtvDs9v3
https://colab.research.google.com/drive/1SxQtfFvg1kXE2ReJdnh5EHA0X6HsktF6
https://colab.research.google.com/drive/1AF6DKbZMVsn5E3v4CJOnJB_jPEnz1W7M
https://documenter.getpostman.com/view/21827988/UzXSuEYn
https://ello.co/7gravitfarcku/post/xuz20af6vr6pvyjbppih6a
https://colab.research.google.com/drive/1u6AMyrZXduW17ETqNFO6m0UCl6qjzHQ1
https://ello.co/ceteqtorno/post/2dgqwylrvtmugf2mnprwpw
https://colab.research.google.com/drive/1aybVjNf3LEZ_TeB6uJ11ZXohawIDn6Ym
https://ello.co/caecomagge/post/lws-poe3qmfu1pee5nnzua
https://colab.research.google.com/drive/10YnIjVy_x4vnyEgpvchcbX_9aZcUb5Eq

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A small supermarket chain has signed a deal with a larger grocery chain to open up to 30 supermarkets across Pennsylvania.

Capital Food Mart, based in Statesboro, Ga., signed an agreement with Giant Eagle Inc. and its subsidiary Giant Eagle Liquor Mart in Monroeville, to open seven stores in Allegheny, Monroe, Westmoreland, Berks, Delaware and York counties.

The expansion was announced Thursday, according to a press release from Capital Food Mart.

“We are incredibly proud to enter the Commonwealth of Pennsylvania with this exciting new venture,” Capital Food Mart CEO R.J. Stroud said in the release. “The support of the Giant family from the beginning of the project has been fantastic, and we are thrilled with the opportunity this presents for our company and our community.”

Stroud said the company would employ about 80 people in those stores, which are projected to open in the next year.

Giant Eagle, which is based in Monroeville, had nearly 1,800 stores across the Pittsburgh area as of the end of last year.Managing Dialog Cards in Azure Bot Framework

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Using the Dialog Model for Building Conversational User Interfaces in Azure Bot Framework

Welcome to The Do’s and Don’ts of Building Microsoft Azure Bot Framework Apps! In this post we will be discussing about the Dialog Model in Azure Bot Framework. What is Dialog Model? How to use Dialog Model? These are the questions which I get most frequently asked from my users. In this blog, I will be walking you
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