Fundamental Theorem of Calculus I Quiz

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F'(x)=f(x) for easy

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Noor Alzoubi

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Fundamental Theorem of Calculus I QuizVersión en línea F'(x)=f(x) for easy por Noor Alzoubi 1 Let F(x)=∫ from 0 to x of t^3 dt. What is F'(x)? a x^2 b t^3 c 3x^2 d x^3 2 Which condition is needed for FTC Part 1 to hold? a f must be continuous on [a,b] b F must be constant c f must be integrable but not continuous d f must be differentiable on [a,b] 3 If F(x)=∫ from 1 to x of sin t dt, F'(π/2) equals what? a sin(π/4) b 0 c cos(π/2) d sin(π/2)=1 4 What is the derivative of F(x)=∫ from 0 to x of e^t dt? a e b e^x c e^0 d x e^x 5 True or false: FTC Part 1 says derivative of an integral with variable upper limit equals the integrand at that upper limit. a Only if the integrand is polynomial b Only if the lower limit also varies c True d False 6 If F(x)=∫ from a to x f(t) dt, what is F'(x) by FTC Part 1? a f(a) b f(x) c ∫ from a to x f(t) dt d F(x) 7 Which concept best describes why F'(x)=f(x) for F(x)=∫_a^x f(t) dt? a Chain rule applied to the upper limit b Integration by parts c CPT symmetry d Average value theorem 8 If f(t)=t, and F(x)=∫ from 0 to x t dt, what is F'(x)? a x b 0 c 1 d 2x 9 Which of the following is an application of FTC Part 1? a Finding antiderivatives without limits b Differentiating an accumulated area function c Integrating a constant d Solving a differential equation

Fundamental Theorem of Calculus I QuizVersión en línea

F'(x)=f(x) for easy

por Noor Alzoubi

Let F(x)=∫ from 0 to x of t^3 dt. What is F'(x)?

x^2

t^3

3x^2

x^3

Which condition is needed for FTC Part 1 to hold?

f must be continuous on [a,b]

F must be constant

f must be integrable but not continuous

f must be differentiable on [a,b]

If F(x)=∫ from 1 to x of sin t dt, F'(π/2) equals what?

sin(π/4)

cos(π/2)

sin(π/2)=1

What is the derivative of F(x)=∫ from 0 to x of e^t dt?

e^x

e^0

x e^x

True or false: FTC Part 1 says derivative of an integral with variable upper limit equals the integrand at that upper limit.

Only if the integrand is polynomial

Only if the lower limit also varies

True

False

If F(x)=∫ from a to x f(t) dt, what is F'(x) by FTC Part 1?

f(a)

f(x)

∫ from a to x f(t) dt

F(x)

Which concept best describes why F'(x)=f(x) for F(x)=∫_a^x f(t) dt?

Chain rule applied to the upper limit

Integration by parts

CPT symmetry

Average value theorem

If f(t)=t, and F(x)=∫ from 0 to x t dt, what is F'(x)?

Which of the following is an application of FTC Part 1?

Finding antiderivatives without limits

Differentiating an accumulated area function

Integrating a constant

Solving a differential equation

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Fundamental Theorem of Calculus I Quiz

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Fundamental Theorem of Calculus I QuizVersión en línea

por Noor Alzoubi

Let F(x)=∫ from 0 to x of t^3 dt. What is F'(x)?

Which condition is needed for FTC Part 1 to hold?

If F(x)=∫ from 1 to x of sin t dt, F'(π/2) equals what?

What is the derivative of F(x)=∫ from 0 to x of e^t dt?

True or false: FTC Part 1 says derivative of an integral with variable upper limit equals the integrand at that upper limit.

If F(x)=∫ from a to x f(t) dt, what is F'(x) by FTC Part 1?

Which concept best describes why F'(x)=f(x) for F(x)=∫_a^x f(t) dt?

If f(t)=t, and F(x)=∫ from 0 to x t dt, what is F'(x)?

Which of the following is an application of FTC Part 1?

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