Calc 1 Chapter 5 and 7.7 (Area and Distance Problems, Definite Integral, Fundamental Theorem of Calculus, Indefinite Integrals and Net Change Theorem, The Substitution rule, Approximate Integration)

How do you find the area under a curve (words)?

approximate the region S by rectangles, then take the limit of the sum of the areas of the approximating rectangles as we increase the number of rectangles

How do you find the area of a rectangle approximation in a curve

find the height (f(x)) of each rectangle and multiply by the width of the base of the rectangle, then add them all together

True or False: You need to find lower and upper estimates of the sum of rectangles in a curve and average them to find the approximate area.

True

What is the equation for finding the width of each of the n strips under a curve?

Δx = (b-a)/n

What is the formula for any sample point in a rectangle?

xi = a + iΔx

What is the general equation associated with this definition:
The area A of the region S that lies under the graph of the continuous function f is the limit of the sum of the areas of approximating rectangles.

A=lim n→∞ [f(x*1)Δx + f(x*2)Δx + … + f(x*n)Δx]

What is A?

the unique number that is smaller than all the upper sums and bigger than all the lower sums

Measure of velocity

d = lim n→100 ∑n,i=1 f(ti-1)Δt = lim n→100 ∑n,i=1 f(ti)Δt

True or False: Distance traveled is equal to the distance formula when accounting for velocity.

False; distance traveled is equal to the area under the graph of the velocity function