Integrals as a limit of rectangle areas

MathematicsCalculusAges 17–18

The area of the curved region below the curve y = f(x) on [a, b] is approximated by n rectangles (left, right, midpoint) or trapezoids. Increase n with the button or slider to watch the sum Sₙ converge to the value of the integral ∫f(x)dx found from an antiderivative; drag the endpoints a and b directly on the graph. Choose the velocity function v(t) to see distance traveled as the integral of velocity.