The average value of x \sqrt{x} x <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> over the interval 0 < x < 2 is

2 3 2 \frac{2}{3}\sqrt{2} 3 2 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

1 3 2 \frac{1}{3}\sqrt{2} 3 1 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

1 2 2 \frac{1}{2}\sqrt{2} 2 1 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

4 3 2 \frac{4}{3}\sqrt{2} 3 4 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

∫ sin ⁡ ( 2 x + 3 ) d x \int_{ }^{ }\sin\left(2x+3\right)dx ∫ sin ( 2 x + 3 ) d x

− 1 2 cos ⁡ ( 2 x + 3 ) + C -\frac{1}{2}\cos\left(2x+3\right)+C − 2 1 cos ( 2 x + 3 ) + C

1 2 cos ⁡ ( 2 x + 3 ) + C \frac{1}{2}\cos\left(2x+3\right)+C 2 1 cos ( 2 x + 3 ) + C

cos ⁡ ( 2 x + 3 ) + C \cos\left(2x+3\right)+C cos ( 2 x + 3 ) + C

− cos ⁡ ( 2 x + 3 ) + C -\cos\left(2x+3\right)+C − cos ( 2 x + 3 ) + C

− 1 5 cos ⁡ ( 2 x + 3 ) + C -\frac{1}{5}\cos\left(2x+3\right)+C − 5 1 cos ( 2 x + 3 ) + C

Integrals Retake

Authored by Janie Cates

Mathematics

12th Grade - University

Used 18+ times

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10 questions

Show all answers

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

$\int_{ }^{ }\left(x^3-3x\right)dx$ =

$3x^2-3+C$

$4x^4-6x^2+C$

$\frac{x^4}{3}-3x^2+C$

$\frac{x^4}{4}-3x^{ }+C$

$\frac{x^4}{4}-\frac{3x^2}{2}+C$

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

The graph of a piecewise-linear function, f, for -1 < x < 4, is shown above. What is the value of $\int_{-1}^4\ f\left(x\right)\ dx$ ?

2.5

5.5

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

The values of a continuous function f for selected values of x are given in the table. What is the value of the left Riemann sum approximation to $\int_0^{50}f\left(x\right)\ dx$ using the subintervals [0, 25], [25, 30], and [30, 50]?

290

360

380

390

430

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

A particle moves along the x-axis. The velocity of the particle at time t is $6t-t^2$ . What is the total distance traveled by the particle from time t = 0 to t = 3?

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

$\int_{ }^{ }\ \frac{x\ dx}{\sqrt{3x^2+5}}$

$\frac{1}{9}\left(3x^2+5\right)^{\frac{3}{2}}+C$

$\frac{1}{4}\left(3x^2+5\right)^{\frac{3}{2}}+C$

$\frac{1}{12}\left(3x^2+5\right)^{\frac{1}{2}}+C$

$\frac{1}{3}\left(3x^2+5\right)^{\frac{1}{2}}+C$

$\frac{3}{2}\left(3x^2+5\right)^{\frac{1}{2}}+C$

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

If $\frac{dy}{dx}=\ \tan\ x$ , then $y\ =\$

$\frac{1}{2}\tan^2x\ +\ C$

$\sec^2x\ +\ C$

$\ln\left|\sec\ x\right|\ +\ C$

$\ln\left|\cos\ x\right|\ +\ C$

$\sec\ x\ \tan\ x\ +\ C$

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

$\int_1^4\ \left|x-3\right|dx$

$-\frac{3}{2}$

$\frac{3}{2}$

$\frac{5}{2}$

$\frac{9}{2}$

$5$

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

The average value of $\sqrt{x}$ over the interval 0 < x < 2 is

$\frac{1}{3}\sqrt{2}$

$\frac{1}{2}\sqrt{2}$

$\frac{2}{3}\sqrt{2}$

$\frac{4}{3}\sqrt{2}$

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

$\int_{ }^{ }\sin\left(2x+3\right)dx$

$\frac{1}{2}\cos\left(2x+3\right)+C$

$\cos\left(2x+3\right)+C$

$-\cos\left(2x+3\right)+C$

$-\frac{1}{2}\cos\left(2x+3\right)+C$

$-\frac{1}{5}\cos\left(2x+3\right)+C$

10.

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

$\int_0^1\left(3x-2\right)^2dx$

$-\frac{7}{3}$

$-\frac{7}{9}$

$\frac{1}{9}$

$1$

$3$

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Integrals Retake

∫(x3−3x)dx\int_{ }^{ }\left(x^3-3x\right)dx∫​(x3−3x)dx =

The graph of a piecewise-linear function, f, for -1 < x < 4, is shown above. What is the value of ∫−14 f(x) dx\int_{-1}^4\ f\left(x\right)\ dx∫−14​ f(x) dx ?

The values of a continuous function f for selected values of x are given in the table. What is the value of the left Riemann sum approximation to ∫050f(x) dx\int_0^{50}f\left(x\right)\ dx∫050​f(x) dx using the subintervals [0, 25], [25, 30], and [30, 50]?

A particle moves along the x-axis. The velocity of the particle at time t is 6t−t26t-t^26t−t2 . What is the total distance traveled by the particle from time t = 0 to t = 3?

∫ x dx3x2+5\int_{ }^{ }\ \frac{x\ dx}{\sqrt{3x^2+5}}∫​ 3x2+5​x dx​

If dydx= tan⁡ x\frac{dy}{dx}=\ \tan\ xdxdy​= tan x , then y = y\ =\ y =

∫14 ∣x−3∣dx\int_1^4\ \left|x-3\right|dx∫14​ ∣x−3∣dx

The average value of x\sqrt{x}x​ over the interval 0 < x < 2 is

∫sin⁡(2x+3)dx\int_{ }^{ }\sin\left(2x+3\right)dx∫​sin(2x+3)dx

∫01(3x−2)2dx\int_0^1\left(3x-2\right)^2dx∫01​(3x−2)2dx

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$\int_{ }^{ }\left(x^3-3x\right)dx$ =

The graph of a piecewise-linear function, f, for -1 < x < 4, is shown above. What is the value of $\int_{-1}^4\ f\left(x\right)\ dx$ ?

The values of a continuous function f for selected values of x are given in the table. What is the value of the left Riemann sum approximation to $\int_0^{50}f\left(x\right)\ dx$ using the subintervals [0, 25], [25, 30], and [30, 50]?

A particle moves along the x-axis. The velocity of the particle at time t is $6t-t^2$ . What is the total distance traveled by the particle from time t = 0 to t = 3?

$\int_{ }^{ }\ \frac{x\ dx}{\sqrt{3x^2+5}}$

If $\frac{dy}{dx}=\ \tan\ x$ , then $y\ =\$

$\int_1^4\ \left|x-3\right|dx$

The average value of $\sqrt{x}$ over the interval 0 < x < 2 is

$\int_{ }^{ }\sin\left(2x+3\right)dx$

$\int_0^1\left(3x-2\right)^2dx$