Integral from t=a to t=b

Definition

The integral from t=a to t=b represents the area under a curve between two points on the x-axis. It calculates the total accumulation of a quantity over a given interval.

Analogy

Think of the integral as measuring how much water is collected in a bucket when it rains for a certain amount of time. The integral from t=a to t=b tells you the total amount of rainwater that falls during that specific time period.

Related terms

Antiderivative: A function whose derivative is equal to the original function. It represents the reverse process of differentiation.

Riemann Sum: An approximation method for finding areas under curves by dividing them into smaller rectangles and summing their areas.

Fundamental Theorem of Calculus: States that if f(x) is continuous on [a, b] and F(x) is an antiderivative of f(x), then ∫[a, b] f(x) dx = F(b) - F(a).