Page 31 - Calculus for the Clueless

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This problem appears to be exactly the same as the last except the x is on top instead of the bottom. This
problem is given to show that the techniques are different, even in problems that look the same—some longer,
some shorter, some easier, some harder. The kind of problem is known only after lots of study. Do them and
hope they are short and easy.

Again let x = 4 sin u. dx = 4 cos u
du.

Notes

As you can see, these two problems are quite different, although they look basically the same.

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We will finish by showing that the area of a circle really is πr . We will find one-quarter the area of the circle x 2
+ y = r and then multiply it by 4.
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Example 14—

x = r sin u; dx = r cos u du.

x = r, r = r sin u, 1 = sin u, u = π/2; x = 0, 0 = r sin u, 0 = sin u, u = 0.