A water tank is filled at a rate of r(t) liters per minute (where t is the time in minutes). What does int_(1)^(7)r^(')(t)dt represent? Choose 1 answer: (A) The rate at which the tank was filled at t=7. B) The average rate of filling between t=1 and t=7. (C) The change in the rate of filling between t=1 and t=7. (D) The amount of water filled between t=1 and t=7.

Understand the integral: Understand the integral of a derivative. The integral of a derivative function over an interval gives us the net change of the original function over that interval. This is based on the Fundamental Theorem of Calculus.Apply Fundamental Theorem: Apply the Fundamental Theorem of Calculus. Since r'(t) is the derivative of r(t), the integral from 1 to 7 of r'(t) dt represents the net change in r(t) from t=1 to t=7.Interpret r(t): Interpret the meaning of r(t). The function r(t) represents the volume of water in the tank at time t. Therefore, the change in r(t) from t=1 to t=7 represents the amount of water that has been added to the tank during this time interval.Choose correct answer: Choose the correct answer. Based on the interpretation in Step 3, the integral from 1 to 7 of r'(t) dt represents the amount of water filled between t=1 and t=7. This corresponds to answer choice (D).

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A water tank is filled at a rate of
r(t) liters per minute (where
t is the time in minutes).
What does
int_(1)^(7)r^(')(t)dt represent?
Choose 1 answer:
(A) The rate at which the tank was filled at
t=7.
B) The average rate of filling between
t=1 and
t=7.
(C) The change in the rate of filling between
t=1 and
t=7.
(D) The amount of water filled between
t=1 and
t=7.

A water tank is filled at a rate of $r(t)$ liters per minute (where $t$ is the time in minutes). $\newline$ What does $\int_{1}^{7} r^{\prime}(t) d t$ represent? $\newline$ Choose $1$ answer: $\newline$ (A) The rate at which the tank was filled at $t=7$ . $\newline$ B) The average rate of filling between $t=1$ and $t=7$ . $\newline$ (C) The change in the rate of filling between $t=1$ and $t=7$ . $\newline$ (D) The amount of water filled between $t=1$ and $t=7$ .

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Calculus

Evaluate definite integrals using the power rule

Full solution

Q. A water tank is filled at a rate of

r(t)

liters per minute (where

t

is the time in minutes).

\newline

What does

\int_{1}^{7} r^{\prime}(t) d t

represent?

\newline

Choose

1

answer:

\newline

(A) The rate at which the tank was filled at

t=7

\newline

B) The average rate of filling between

t=1

and

t=7

\newline

t=1

and

t=7

\newline

(D) The amount of water filled between

t=1

and

t=7

Understand the integral: Understand the integral of a derivative. The integral of a derivative function over an interval gives us the net change of the original function over that interval. This is based on the Fundamental Theorem of Calculus.
Apply Fundamental Theorem: Apply the Fundamental Theorem of Calculus. $\newline$ Since $r'(t)$ is the derivative of $r(t)$ , the integral from $1$ to $7$ of $r'(t) ext{ d}t$ represents the net change in $r(t)$ from $t=1$ to $t=7$ .
Interpret $r(t)$ : Interpret the meaning of $r(t)$ . The function $r(t)$ represents the volume of water in the tank at time $t$ . Therefore, the change in $r(t)$ from $t=1$ to $t=7$ represents the amount of water that has been added to the tank during this time interval.
Choose correct answer: Choose the correct answer. $\newline$ Based on the interpretation in Step $3$ , the integral from $1$ to $7$ of $r'(t) ext{ d}t$ represents the amount of water filled between $t=1$ and $t=7$ . This corresponds to answer choice (D).