Right Riemann sum animation


– THIS IS A RIGHT
REIMANN SUM ANIMATION. THE FUNCTION IS F(X)=X SQUARED
AND THAT WOULD BE THE VELOCITY FUNCTION AND WE’RE ESTIMATING
THE DISTANCE TRAVELED BY AN OBJECT ON A TIME INTERVAL
FROM 0 TO 4 SECONDS LET’S SAY. SO WATCH THE NUMBER OF
RECTANGLES CHANGE REPRESENTING THE NUMBER OF SUB-INTERVALS
THAT WE HAVE FROM 0 TO 4.   THE MORE SUB-INTERVALS YOU HAVE,
WHICH EQUALS THE NUMBER OF RECTANGLES,
THE SUM IS COMING DOWN TO THE IDEAL AND WE HAD ONLY
26 RECTANGLES BUT OF COURSE THE NUMBER OF RECTANGLES IS
IDEALY GOING TO GO TO INFINITY AND WHEN IT DOES GO TO INFINITY,
SOMETHING THAT WE’LL LEARN, THE ACTUAL INTEGRAL, THE
DEFINATE INTEGRAL/THE X VALUES FROM 0 TO 4 WILL ACTUALLY
EQUAL 21.33333. AND THE RIGHT SUMS, YOU CAN SEE
IT, IS AN OVER ESTIMATE. THESE RECTANGLES ARE A LITTLE
BIT OVER AND IT SHOWS UP WITH THE NUMBER 22.58 WHEN YOU HAVE
26 RECTANGLES. YOU CAN SEE THAT WHEN THE NUMBER
OF RECTANGLES WENT TO INFINITY THESE WOULD BE JUST TOTALLY
SOLID HERE AND IT WOULD COME RIGHT DOWN ONTO THE GRAPH
OF THE FUNCTION ITSELF. YOU BASICALLY WOULD JUST HAVE
THIS AREA UNDERNEATH THE FUNCTION BEING
THE ACTUAL SUM AND THE LIMIT.  

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