1. Several statements about the definite integral of a continuous function f(x) over [a, b] are written be- low. Determine those statements that are true by writing "TRUE" and those that are false by writing "FALSE." (No work need be included with this question.) t * f(x) dx = F(b)-F(a) where F² = f.. I. One of the Fundamental Theorems of Calculus states that 1. [ f(x) dx = -√" f(x) dr.. III. [ f(z) dr denotes all possible anti-derivatives of f(x). IV. [*f'(sin x) · cos z dr = f(sin(b)) – ƒ(sin(a)). . V. One of the Fundamental Theorems of Calculus states that + ½ / ( √ [ f(t) dt) = f(x)..
1. Several statements about the definite integral of a continuous function f(x) over [a, b] are written be- low. Determine those statements that are true by writing "TRUE" and those that are false by writing "FALSE." (No work need be included with this question.) t * f(x) dx = F(b)-F(a) where F² = f.. I. One of the Fundamental Theorems of Calculus states that 1. [ f(x) dx = -√" f(x) dr.. III. [ f(z) dr denotes all possible anti-derivatives of f(x). IV. [*f'(sin x) · cos z dr = f(sin(b)) – ƒ(sin(a)). . V. One of the Fundamental Theorems of Calculus states that + ½ / ( √ [ f(t) dt) = f(x)..
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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please explain
![1.
Several statements about the definite integral of a continuous function f(x) over [a, b] are written be-
low. Determine those statements that are true by writing "TRUE" and those that are false by writing "FALSE." (No work
need be included with this question.)
I. One of the Fundamental Theorems of Calculus states that
+ [²1(2)
f(x) dx = F(b)-F(a) where F' = f.
II.
· ["f(x) dx = - * f(x) dx.
III.
[ f(x) dr
da denotes all possible anti-derivatives of f(x).
IV.
f'(sin x) · cos z dr = f (sin(b)) — ƒ(sin(a)). .
d
V. One of the Fundamental Theorems of Calculus states that • ( [*1 (1) dt) = f(x)..
f(t)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff5b0c89c-181c-473a-bc63-aaa847ced86c%2F7950ab6b-6c3b-42b7-9e25-cb17c41bd863%2Fpld3gnv_processed.png&w=3840&q=75)
Transcribed Image Text:1.
Several statements about the definite integral of a continuous function f(x) over [a, b] are written be-
low. Determine those statements that are true by writing "TRUE" and those that are false by writing "FALSE." (No work
need be included with this question.)
I. One of the Fundamental Theorems of Calculus states that
+ [²1(2)
f(x) dx = F(b)-F(a) where F' = f.
II.
· ["f(x) dx = - * f(x) dx.
III.
[ f(x) dr
da denotes all possible anti-derivatives of f(x).
IV.
f'(sin x) · cos z dr = f (sin(b)) — ƒ(sin(a)). .
d
V. One of the Fundamental Theorems of Calculus states that • ( [*1 (1) dt) = f(x)..
f(t)
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