Definite Integrals Quiz

Authored by Robert Signs

Mathematics

12th Grade

CCSS covered

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10 questions

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MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Not possible

MULTIPLE CHOICE QUESTION

1 min • 1 pt

-1

-2

1/2

-1/2

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Using 5 subintervals, calculate the distance traveled using a left sum.

360

420

396

390

Evaluate the definite integral.

9/2

Not possible

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Evaluate the definite integral.

Not possible

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Let $F\left(x\right)=\int_0^xf\left(t\right)dt$ , where the graph of $f\left(x\right)$ above consists of lines and a semi-circle. Determine $F\left(4\right)$ .

$\pi$

$2\pi$

$3\pi$

$4\pi$

FILL IN THE BLANKS QUESTION

30 sec • 1 pt

Evaluate the definite integral below using a graphing calculator. Leave answer as a decimal and round to three decimal places.

$\int_0^{\frac{\pi}{4}}\ \sin\left(-3x+12\right)\ dx$

(a)

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

$If\ \ \int_{-2}^5f\left(x\right)dx\ =\ -3\ \ \ \ \ \$ What is the value of $\int_5^{-2}f\left(x\right)dx\ =$

-3

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

$\int_1^2\left(4-x\right)dx=$

2.5

$-\frac{5}{2}$

$\frac{2}{5}$

$-0.4$

10.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

$\int_1^3\left(2-\frac{3}{x^2}\right)dx=$

$-\frac{1}{2}$

$-2$

$0.5$

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Definite Integrals

Using 5 subintervals, calculate the distance traveled using a left sum.

Evaluate the definite integral.

Evaluate the definite integral.

Let F(x)=∫0xf(t)dtF\left(x\right)=\int_0^xf\left(t\right)dtF(x)=∫0x​f(t)dt , where the graph of f(x)f\left(x\right)f(x) above consists of lines and a semi-circle. Determine F(4)F\left(4\right)F(4) .

Evaluate the definite integral below using a graphing calculator. Leave answer as a decimal and round to three decimal places. ∫0π4 sin⁡(−3x+12) dx\int_0^{\frac{\pi}{4}}\ \sin\left(-3x+12\right)\ dx∫04π​​ sin(−3x+12) dx (a)

If ∫−25f(x)dx = −3 If\ \ \int_{-2}^5f\left(x\right)dx\ =\ -3\ \ \ \ \ \ If ∫−25​f(x)dx = −3 What is the value of ∫5−2f(x)dx =\int_5^{-2}f\left(x\right)dx\ =∫5−2​f(x)dx =

∫12(4−x)dx=\int_1^2\left(4-x\right)dx=∫12​(4−x)dx=

∫13(2−3x2)dx=\int_1^3\left(2-\frac{3}{x^2}\right)dx=∫13​(2−x23​)dx=

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Let $F\left(x\right)=\int_0^xf\left(t\right)dt$ , where the graph of $f\left(x\right)$ above consists of lines and a semi-circle. Determine $F\left(4\right)$ .

Evaluate the definite integral below using a graphing calculator. Leave answer as a decimal and round to three decimal places.

$\int_0^{\frac{\pi}{4}}\ \sin\left(-3x+12\right)\ dx$

(a)

$If\ \ \int_{-2}^5f\left(x\right)dx\ =\ -3\ \ \ \ \ \$ What is the value of $\int_5^{-2}f\left(x\right)dx\ =$

$\int_1^2\left(4-x\right)dx=$

$\int_1^3\left(2-\frac{3}{x^2}\right)dx=$