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AP Exams AP Calculus Integrals Easy Practice Question

Learn + Solve: Shortcut, Trap & Fast Route Click to view shortcut, steps, and common mistake

Shortcut used: Identify whether the problem needs an antiderivative, definite integral, approximation, or accumulation theorem.

Solve in 3 steps:

Mark the given values and the exact target.
Apply the relevant formula, rule, or concept.
Check the final value against the options.

Common mistake: Do not choose an option before confirming the exact demand of the question.

Question 3 Multiple Choice Question

Question

If F(x)=∫ from 1 to x of (t^2+1) dt, what is F'(x)?

Explanation

Correct Answer: C

ANSWER

Correct Answer: C

Method / Topic: Integrals

By the Fundamental Theorem of Calculus, the derivative equals the integrand evaluated at x.

Why this answer is correct

The correct option matches the required rule and the given information.

Short Explanation

By the Fundamental Theorem of Calculus, the derivative equals the integrand evaluated at x.

Detailed Explanation

Question

If F(x)=∫ from 1 to x of (t^2+1) dt, what is F'(x)?

ANSWER

Correct Answer: C

Method / Topic: Integrals

By the Fundamental Theorem of Calculus, the derivative equals the integrand evaluated at x.

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Question 3

Easy Marks: 1.0 Practice Question

Learn + Solve: Shortcut, Trap & Fast Route Click to view shortcut, steps, and common mistake

Shortcut used: Identify whether the problem needs an antiderivative, definite integral, approximation, or accumulation theorem.

Solve in 3 steps:

Mark the given values and the exact target.
Apply the relevant formula, rule, or concept.
Check the final value against the options.

Common mistake: Do not choose an option before confirming the exact demand of the question.

Question

If F(x)=∫ from 1 to x of (t^2+1) dt, what is F'(x)?

Explanation

Correct Answer: C

ANSWER

Correct Answer: C

Method / Topic: Integrals

By the Fundamental Theorem of Calculus, the derivative equals the integrand evaluated at x.

Why this answer is correct

The correct option matches the required rule and the given information.

Short Explanation

By the Fundamental Theorem of Calculus, the derivative equals the integrand evaluated at x.

Detailed Explanation

Question

If F(x)=∫ from 1 to x of (t^2+1) dt, what is F'(x)?

ANSWER

Correct Answer: C

Method / Topic: Integrals

By the Fundamental Theorem of Calculus, the derivative equals the integrand evaluated at x.

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definite integral approximation or accumulation theorem.

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