Let f(t) = t. a. What expression would represent f(t)dt b. Let F(x) = f(t)dt. Find...

 

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Let f(t) = t². a. What expression would represent f(t)dt b. Let F(x) = f(t)dt. Find F'(x). 9=110 c. What is the difference between f(t) = t² and your answer from part "b"? d. Would you agree that if F(x) = f(t)dt, then F'(x) = f(x)? Part "d" is the first Fundamental Theorem of Calculus. It relates the two big ideas in calculus, derivatives, and integrals. (Note f(t) must be continuous on [a, x]) e. F'(t) = f(t) is shown below. Use the First Fundamental Theorem of Calculus to find F'(3) y = f(t) 2 3 Let f(t) = t². a. What expression would represent f(t)dt b. Let F(x) = f(t)dt. Find F'(x). 9=110 c. What is the difference between f(t) = t² and your answer from part "b"? d. Would you agree that if F(x) = f(t)dt, then F'(x) = f(x)? Part "d" is the first Fundamental Theorem of Calculus. It relates the two big ideas in calculus, derivatives, and integrals. (Note f(t) must be continuous on [a, x]) e. F'(t) = f(t) is shown below. Use the First Fundamental Theorem of Calculus to find F'(3) y = f(t) 2 3