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Find the exact area of the surface obtained by rotating the curve about the x-axis.

$ y = \sqrt{1 + e^x} $ , $ 0 \le x \le 1 $

$$

\pi(1+e)

$$

Applications of Integration

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Missouri State University

University of Michigan - Ann Arbor

Idaho State University

we no formal. We're gonna be using his intro from A to B to par. Why d us know. What we know is that our squared of one plus you to the axe is because it is gonna become one plus e to the X over to because we don't want the square root or more plugging into the formula and makes it a lot more complicated to read. So one plus either the axe over too Times D Backs member. It's important that we're following this formula over here. This is the same thing as two part comes expose you to the axe divided by two. Remember in Vieques over to taking the Inderal? It's still eating the X over two. He's kind of a special case. If you don't remember all the properties of the I would recommend reading up on it. But it's a special case that you should have learned about in a previous math class. Plugging in to part times one pussy over to minus 1/2 gives us pi times one plus e. And then this is the exact answer so we can leave this us