Facts Assessment Flashcards
Calc
1
Q
∫ x^n dx
A
(x^( n+1 )) / (n+1) + c, where n ≠ 1
2
Q
∫ 1 / (x^n) dx
A
(x^(-n+1)) / (-n+1) + c, where n ≠ 1
3
Q
∫ 1 / x dx
A
lnlxl + c
4
Q
∫ e^x dx
A
e^x + c
5
Q
∫ a^x dx
A
(a^x) / lna + c
6
Q
∫ sinx dx
A
-cosx + c
7
Q
∫ cosx dx
A
sinx + c
8
Q
∫ sec^2 x dx
A
tanx + c
9
Q
∫ secxtanx dx
A
secx + c
10
Q
∫ cscxcotx dx
A
-cscx + c
11
Q
∫ csc^2 x dx
A
-cotx + c
12
Q
What is the slope formula for parametric curves?
A
dy/dx = (dy/dt)/(dx/dt)
13
Q
What is the formula for the 2nd derivative, d^2y/dx^2, for a parametric curve?
A
((dx/dt)(d^2y/dx^2)-(dy/dt)(d^2x/dt^2))/(dx/dt)^3
14
Q
What is the arc length for a function, y=f(x)?
A
∫b/a √(1 + (dy/dx)^2)dx
15
Q
What is the arc length formula for a parametric curve?
A
∫b/a √((dx/dt)^2 + (dy/dt)^2)dt
