Unit 6 Integration and accumulation of change
formula for area of a trapezoid
A=1/2h(b1+b2)
Area of a circle
A=πr²
(6.7) Antiderivatives = backwards derivative
don't forget pablo! +C
Derivatives and integrals are ____ of each other
inverses. They cancel eachother out
Antiderivative of 1/x
ln|x| anytime natural log is your antiderivative, remember to use absolute value bars
Trapezoidal Sum
An approximation method a= 1/2 (b1+b2)h
(6.2) Left and Right riemann sums
An approximation method. a=bh
On a trapezoid estimation, when does it underestimate?
when the function is concave down
On a trapezoid estimation, when does it overestimate?
when the function is concave up
Antiderivative of xⁿ
xⁿ+1 / n+1
Fundamental Theorem of Calculus
∫ f(t) dt on interval a to x = f(x) & ∫ f(x) dx on interval a to b = F(b) - F(a)
(6.1) Area under a curve
∫ f(x) dx integrate over interval a to b (accumulation of change)
(6.4) Accumulation Functions ex: F(x) = ∫ t^3 on interval 2 to x dt find F'(x)
F'(x) = x^3 (replace t with x)
On a decreasing function, which riemann sum overestimates?
The left riemann sum
On an increasing function, which riemann sum underestimates?
The left riemann sum
On a decreasing function, which riemann sum underestimates?
The right riemann sum
On an increasing function, which riemann sum overestimates?
The right riemann sum
(6.6) properties of definite integrals
super easy concept, just review
