Solve The Problem
Fix the Error
Definitions
Area between two Curves
Miscellaneous
100
9 9 9 ∫f(x)dx=-1 ∫f(x)dx=5 ∫h(x)dx=4 1 7 7 9 Find ∫-2f(x)dx. 1
What is 2?
100
If ∫(x+5)^5 dx where u=x+2 and du=1dx , the answer is ((x+2)^6)/6 .
What is ((x+2)^6)/6 +C? What is +C?
100
A function of which a given function is the derivative and yields that function when differentiated?
What is an Integral?
100
y=1- x^2 y=sinx Find area between the curves and use a calculator!
What is 1.670 ?
100
(f*g)'= ____
What is (f'*g) + (g'*f)?
200
∫dy/dx=∫lnx x=5 y=2 x=5 y=∫ln(t) dt +c 5 Find C.
What is 2?
200
∫tanxdx = ∫(sinx/cosx)dx u = cosx du = -sinxdx -du/sinx = dx ∫(sinx/u) * (-du/sinx) -ln|u|+C
What is -ln|cosx|+C ?
200
Acceleration is ___ to Position.
What is the Second Derivative?
200
y=x^2 - 2 y=2 Find area between two curves
What is 10.666 ?
200
(f(g(x)))'=f'(g(x))g'(x)
What is the Chain Rule?
300
y=(x-1)^2 [0,3] b f(c)=(1/b-a)∫f(x)dx a Find c.
What is 0,3?
300
∫ds/dt = ∫t^2 +1 (t,s) t=0 , s=1 (0,1) s=(t^3)/3 +t
What is s=(t^3)/3 +t+1? or What is +1 ?
300
Synonym: Antiderivative.
What is an Indefinite Integral?
300
y=-x y=2-(x^2) [-1,2]
What is 9/2?
300
The Inverse of a Derivative.
What is 1/(f'(x))?
400
f'(x)= xsin(x) Find f(x)
What is -xcos(x)+sin(x)+C ?
400
3 u=3x^2 du=6xdx du/6x=dx ∫6xsin(3x^2)dx 1 ( 6xcos(u))/6x ((6cos(3^2*3)) - ((6cos(1^2*3) = 4.187 Two errors and real answer?
What is forgetting the negative sign and dividing by 6? and what is -0.697
400
If f is a continuous function on an open interval for 'I' and 'a' any point in 'I', and F is defined by x F(x)=∫f(t)dt, a and F'(x)=f(x) at each point in 'I' where F'(x) is the derivative of F(x), then ___ is in effect.
What is the Second Fundamental Thereom of Calculus?
400
y=x^2 -1 y=2cosx [-1.265424, 1.265423]
What is 4.99?
400
what is 202.
What is Mrs. Favorite's Room?
500
The graph of f' has the areas: A=3 for[0,2] B=-12 for [2,7] C=4.5 for [7,10] and x=12 at t=0, find the total distance traveled.
What is 19.5?
500
5 ∫3(t)^2+5(t)-9 dt = (3(t)^3)/3 +(5(t)^2)/2 -9t 0 3*(5)^3 +(5(5^2)/2) +9(5) - 3*0^3 +5(0^2)/2 - 9(0) =232.5
What is +9(5)?
500
Integration by Parts Formula.
What is uv-∫vdu?
500
y=sec^2 (x) y= sin(x) [0, pi/4]
What is the squareroot of two over two?
500
Calculus is _____________________________ .
What is the study of change? / What is the branch of mathematics involving change?
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