Build an antiderivative F(x) of f(x) = eex satisfying F(8) = 0.
Build an antiderivative F(x) of f(x) = eex satisfying F(8) = -1.
We take the antiderivative from the first problem and add -1:
Build an antiderivative of cos x that is 0 when x = 9.
This problem is asking for a function F(x) that is an antiderivative of f(x) = cos x and satisfies F(9) = 0. We know how to do this:
Actually, in this case we could finish integrating and get a nice formula:
Build an antiderivative of sin(x2) that is 3 when x = 8.
is an antiderivative of sin(x2) that is 0 when x = 8. Since we want an antiderivative that equals 3 when x = 8, we just add 3 to this integral:
Make it rain.
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