What you know will help you ,what you don't won't hurt you. Change of variable technique

Solving a functional equation that depends on integrals using the fundamental theorem of calculus
The fundamental theorem of calculus is very important in solving problems that deal with the derivatives Of some functions that are defined by some integrals. The mean value of integrals is also very important in solving some problems. Here we are trying to solve functional equatSolving a functional equation that depends on integrals using the fundamental theorem of calculus
The fundamental theorem of calculus is very important in solving problems that deal with the derivatives Of some functions that are defined by some integrals. The mean value of integrals is also very important in solving some problems. Here we are trying to solve functional equations that depend on some integrals. We will have to use the fundamental theorem of calculus. We will use a change of variable and integration by part. Sometimes we have to use the integration by part more than one time, The change of valuable must be adequate to the problem. One solving, this kind of problems. The fundamental theorem of calculus is your is useful. We can use the fractional decomposition in our case, to find the values, To study the concavity of the function. We find the second derivative which if the second derivative is positive. The function is c8oncave up. If the second derivative is negative, the the concavity is down To see that our function is positive, or in is increasing. We find the derivative. If the first derivative is positive, that means of our function is increasing. And if it is zero, that means that we have some critical values critical points that we have to determine later.
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