If A(x) = ∫₁^x (t^2 + 1) dt, what is A'(2)?

Definite Integrals & Area · Question 9 of 71

Question 9

MediumOriginal question

If $A(x) = \int_1^x (t^2 + 1)\,dt$ , what is $A'(2)$ ?

0

Correct answerYour answer

\frac{10}{3}

Correct answerYour answer

4

Correct answerYour answer

5

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

By the first fundamental theorem, $A'(x) = x^2 + 1$ : the area function's derivative is the integrand at the upper limit.
$A'(2) = 4 + 1 = 5$ .

Worth noting

$\frac{10}{3}$ is $A(2)$ , the integral itself, not its derivative.

Ten questions from Definite Integrals & Area, at your own pace.

Ten questions from Definite Integrals & Area, at your own pace.