Home » Blog » Compute the value of a function given by an integral formula

# Compute the value of a function given by an integral formula

Compute for each of the following continuous functions .

1. .
2. .
3. .
4. .

1. Since we take the derivative of both sides to obtain Therefore, 2. Since we take the derivative of both sides (see part (b) of this exercise for taking the derivative of an integral like this) to obtain Thus, 3. Here we have Here we evaluate the integral on the left, Therefore, Thus, 4. Finally, since we take the derivative of both sides, Then, since (since the cubic polynomial has only one real root at ) we have ### One comment

1. Anonymous says:

Is it necessary to point out that the polynomial x^3 + x^2 = 2 has only one (real) solution? It seems to me that we have already shown that f(x^3+x^2)=1/(3x^2+2x) for all x >= 0. The number 1 is then simply one such number that just happens to give us the particular solution that we are looking for. If there was another y != x such that y^3 + y^2 = 2, it seems to me like it shouldn’t invalidate our solution.