Calculus 1 Final Exam Answered Correctly!!!
1. Fundamental Theorem of Calculus +f(x) dx on interval a to b = F(b) - F(a)
2. Mean Value Theorem for Integrals If f is continuous on [a,b], then
there exists a c in [a,b] such that
integral from a to b of f(x) dx = f(c)(b-a).d
3. Average Value of a Function 1/b-a (integral a-b) f(x)dx
(the value f(c) from the
Mean Value Theorem for
Integrals)
4. (integral a-x) f(t)dt F(x) - F(a)
5. Second Fundamental F(x) = integral from a to x of
Theorem of Calculus f(t)dt F'(x) = f(x)
6. The Net Change Theorem The definite integral of the rate of change of a quantity
F'(x)
gives the total change, or net change, in that quantity
on the interval [a,b].
7. Displacement the net change of the position function ( definite
integral of velocity )
8. Total distance traveled (+a to b) |v(t)|dt
9. Antidifferentiation of a Composite f+(g(x))g'(x)dx = F(g(x)) + C
Function f+(u)du = F(u) + C
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1. Fundamental Theorem of Calculus +f(x) dx on interval a to b = F(b) - F(a)
2. Mean Value Theorem for Integrals If f is continuous on [a,b], then
there exists a c in [a,b] such that
integral from a to b of f(x) dx = f(c)(b-a).d
3. Average Value of a Function 1/b-a (integral a-b) f(x)dx
(the value f(c) from the
Mean Value Theorem for
Integrals)
4. (integral a-x) f(t)dt F(x) - F(a)
5. Second Fundamental F(x) = integral from a to x of
Theorem of Calculus f(t)dt F'(x) = f(x)
6. The Net Change Theorem The definite integral of the rate of change of a quantity
F'(x)
gives the total change, or net change, in that quantity
on the interval [a,b].
7. Displacement the net change of the position function ( definite
integral of velocity )
8. Total distance traveled (+a to b) |v(t)|dt
9. Antidifferentiation of a Composite f+(g(x))g'(x)dx = F(g(x)) + C
Function f+(u)du = F(u) + C
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