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Evaluate the subsequent integral.
Solution
This is an innocent enough looking integral. Though, because infinity is not a real number we cannot just integrate as normal and after that "plug in" the infinity to get the answer, to see how we are going to do this type of integral let's think of this like an area problem. Thus in place of asking what the integral is, let's in place of ask what the area within f (x) = 1/x2 on the interval [1, ∞] is. Till we are not able to do this, though, let's step back a little and instead ask what the area within f (x) is on the interval [1, t] where 1 > t and t is finite. This is a difficulty that we can do.
Now, we can get the area under f(x) on [1, ∞] simply by taking the limit of at like t goes to infinity.
After that this is how we will do the integral itself.
Find out the surface area of the solid acquired by rotating y = √ (9-x 2 ), - 2 x 2 about the x-axis. Solution The formula that we'll be using here is, S = ∫ 2Πyds
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