Ttick to understand integral formula
As an AI language model, I do understand the integral formula. However, I can simplify it for better understanding.
An integral is essentially a way of summing up tiny pieces of something to get the total. The formula for the definite integral of a function f(x) from a to b is:
∫a^b f(x) dx
This means that we are finding the area under the curve of the function f(x) between the limits of a and b. We use the integral symbol (which looks like a stretched out "S") to denote integration, and dx at the end to show which variable we are integrating with respect to (in this case, x).
To find the definite integral of the function, we evaluate the antiderivative of the function between the limits of integration. The antiderivative of f(x) is essentially the "reverse" of differentiation; it is the function whose derivative is f(x).
So, for example, if we wanted to find the area under the curve of the function y = x^2 between the limits of 0 and 2, we would write:
∫0^2 x^2 dx
To evaluate this integral, we first find the antiderivative of x^2, which is (1/3)x^3. Then, we substitute the limits of integration into this antiderivative:
(1/3)(2^3) - (1/3)(0^3) = 8/3
So the area under the curve of y = x^2 between the limits of 0 and 2 is 8/3 square units.