Question
What is the average (mean) value of \(3t^{3}-t^{2} \)over the interval\( -1\leq t\leq 2 \)?
(A)\(\frac{11}{4} \) (B)\(\frac{7}{2} \) (C)8 (D)\(\frac{33}{4}\) (E) 16
▶️Answer/Explanation
Ans:A
Question
The average value of \(\sqrt{x}\) over the interval 0 ≤ 2 ≤ x is
(A)\(\frac{1}{3}\sqrt{2}\) (B)\(\frac{1}{2}\sqrt{2}\) (C)\(\frac{2}{3}\sqrt{2} \) (D) 1 (E)\(\frac{4}{3}\sqrt{2}\)
▶️Answer/Explanation
Ans:C
Question
If the position of a particle on the x-axis at time t is \(−5t^{2}\) , then the average velocity of the particle for 0 ≤ t ≤ 3 is
(A) −45 (B) −30 (C) −15 (D) −10 (E) −5
▶️Answer/Explanation
Ans:C
Let \(x(t)=5t^2\) be the position at time t. Average velocity\frac{x(3)-x(0)}{3-0}=\frac{-45-0}{3}=-15\)
Question
What is the average value of \(y=x^2\sqrt{x^3+1}\) on the interval [0, 2] ?
(A) \(\frac{26}{9}\) (B)\(\frac{52}{9}\) (C) \(\frac{26}{3}\) (D) \(\frac{52}{3}\) (E) 24
▶️Answer/Explanation
Ans:A
Question
What is the average value of y for the part of the curve\( y= 3x-x^{2}\) which is in the first quadrant ?
(A) –6 (B) –2 (C) \(\frac{3}{2}\) (D) \(\frac{9}{4}\) (E)\(\frac{9}{2}\)
▶️Answer/Explanation
Ans:C
