Integration Theory Flashcards
If f β(x) = g(x) what is the antiderivative of g(x)?
f(x)+C
What is β« π^π₯ ππ₯?
e^x + C
What is β« sin(π₯) ππ₯?
-cos(x) + C
What is β« cos(π₯) ππ₯?
sin x + C
What is β« 1/π₯ ππ₯
ln|x| + C
What is β« sec(π₯) tan(π₯) ππ₯?
sec x + C
What is β« sec^2 (π₯) ππ₯?
tan x + C
What is β« 4π₯^5 ππ₯?
2/6 x^6 + C
What is β« 3π₯^-7ππ₯?
β 1/2 π₯^β6 + πΆ
Whatβs the antiderivative of velocity?
Position
Whatβs the antiderivative of acceleration?
Velocity
Knowing the force, whatβs the acceleration?
a = F/m
What is β« 1/(1+π₯^2) ππ₯?
arctan(π₯) + πΆ
What is β« 1/(β1βπ₯^2) ππ₯?
arcsin(x)+C
What is β« 1/(|π₯|βπ₯^2 β1) ππ₯?
arcsec(π₯) + πΆ
What is Areaβ?
f(x)
if the area under a graph is x^3, whatβs the function?
f(x) = 3x^2
If Aο’(x) = f(x) then what is A(x)?
The antiderivative of f(x)
Let A(x) be the area from 2 to x under f(x). If A(x) = F(x) + C, what is C?
-F(2)
What is (2x+1)|5
|2
(2 Γ 5 + 1) β (2 Γ 2 + 1) = 6
