medium
2 min read
Definite Integral
Definite Integral A definite integral , also called an antiderivative , is the inverse operation of differentiation. It takes a function and returns an...
Quick Actions
Insights
Difficultymedium
Reading Time2 min
Definite Integral A definite integral , also called an antiderivative , is the inverse operation of differentiation. It takes a function and returns an...
A definite integral, also called an antiderivative, is the inverse operation of differentiation. It takes a function and returns another function that has the original function's derivative.
Formally, the definite integral of a function f(x) with respect to x from a to b is denoted by:
This means we are finding the area under the graph of f(x) between x = a and x = b.
Examples:
This means the area of the region under the graph of f(x) = x^2 between x = 0 and x = 4 is 16 square units.
This means that the area under the graph of f(x) = 1/x between x = 1 and x = infinity is infinite.
Key Points:
A definite integral is a calculation of the area under the graph of a function.
It is the inverse operation of differentiation.
The definite integral of a function with respect to x from a to b is denoted by an integral sign from a to b.
Definite integrals can be evaluated by finding the area under the graph of the function