All Flashcards
Explain how the area under a velocity-time graph relates to distance.
The area under a velocity-time graph represents the total distance traveled.
What does a definite integral calculate?
The exact area under a curve between two specified limits.
Why are Riemann Sums approximations?
Riemann Sums use rectangles to approximate the area, which may not perfectly match the curve, leading to over or underestimations.
How do integrals 'undo' derivatives?
Integration is the reverse process of differentiation; it finds the original function before differentiation.
Define accumulation of change.
The sum, over time, of how much something has changed.
What is a Riemann Sum?
A method of approximating the area under a curve by dividing it into rectangles or other simple shapes.
Define definite integral.
An integral with upper and lower limits, representing the area under a curve between those limits.
What are integrals also called?
Anti-derivatives.
What is the meaning of 'signed area'?
Area below the x-axis is considered negative, representing a decrease or movement in the opposite direction.
What is the formula for distance given constant velocity and time?
What is the formula for the area of a rectangle?
What is the formula for the area of a triangle?
What is the formula for the area of a trapezoid?