How do you find the absolute min and max of an integral?

How do you find the maximum value of a definite integral?

How do you find the absolute maximum?

Finding the Absolute Extrema
  1. Find all critical numbers of f within the interval [a, b]. …
  2. Plug in each critical number from step 1 into the function f(x).
  3. Plug in the endpoints, a and b, into the function f(x).
  4. The largest value is the absolute maximum, and the smallest value is the absolute minimum.

How do you find the minimum of an integral?

To find the minimum, compute the second derivative and determine its sign at the points b_1 = log(1*p/2) and b_2 = log(3*pi/2): F”(b) = -sin(eb)eb , which is negative at b_1 (local maximum) and positive at b_2 (local minimum). In conclusion, the value of b for which the integral is minimum is b = log(3*pi/2).

How do you find the integral of increase and decrease?

The derivative of a function may be used to determine whether the function is increasing or decreasing on any intervals in its domain. If f′(x) > 0 at each point in an interval I, then the function is said to be increasing on I. f′(x) < 0 at each point in an interval I, then the function is said to be decreasing on I.

How do you take the derivative of an integral?