Final answer:
To estimate the integral, we can use the Riemann sum or the Fundamental Theorem of Calculus. The Riemann sum approximates the integral using rectangles, while the Fundamental Theorem of Calculus allows us to find exact values of definite integrals. The indefinite integral, also known as the antiderivative, represents all possible antiderivatives of a function.
Step-by-step explanation:
To estimate the integral using the maxima and minima of a function, we can use the Riemann sum. The Riemann sum is a sum of areas of rectangles that approximate the function over a given interval. This can be done by dividing the interval into smaller subintervals and choosing a sample point within each subinterval. The sum of the areas of the rectangles gives an estimate of the integral.
The definite integral is the exact value of the integral of a function over a given interval. It can be calculated using techniques like the Fundamental Theorem of Calculus or finding antiderivatives. The definite integral gives the net area under the curve of a function.
The indefinite integral is also known as the antiderivative. It gives a family of functions that have a given function as their derivative. The indefinite integral does not have upper and lower limits, unlike the definite integral. It represents all possible antiderivatives of a function.
The Fundamental Theorem of Calculus allows us to calculate definite integrals by finding antiderivatives. It states that if F is an antiderivative of a function f on an interval [a, b], then the definite integral of f(x) from a to b is equal to F(b) - F(a). This theorem is useful for finding exact values of definite integrals.