Antiderivatives Lesson Slides: 7 Slides (Grade 12)

7 Slides • 16 Questions

1

6.3 Definite Integrals and
Anti-derivatives

2

Properties of Definite Integrals

3

Properties of Definite Integrals

4

Multiple Choice

What is the meaning of the following symbol:

$\int_a^bf\left(x\right)\ dx$

1

The area from the curve to the x-axis from x = a to x = b

2

The rate at which f(x) is changing from x = a to x = b

3

The volume when the curve is rotated about the x-axis from x = a to x = b

5

Multiple Choice

Evaluate:

1

9

2

11

3

-11

6

Multiple Choice

Evaluate:

1

9

2

11

3

-2

7

Multiple Choice

Evaluate:

1

28

2

14

3

-2

8

Multiple Choice

Evaluate:

1

-5

2

23

3

-2

9

Multiple Choice

Evaluate:

1

-5

2

23

3

0

10

Multiple Choice

Evaluate:

1

2

32

3

0

11

Multiple Choice

Evaluate:

1

2

3

12

Multiple Choice

Evaluate:

1

2

3

13

14

Average Value of a Function

15

Multiple Choice

f(x)=4-x² over [0,3] find the average value of the function.

1

3

2

12

3

1

16

Multiple Choice

f(x)=x² -1 , over $\left[0,\sqrt[]{3}\right]$ find the average value of the function.

1

3

2

12

3

1

17

Finite Integral of Trigonometric Functions

18

Multiple Choice

$19.\ \int_{\pi}^{2\pi}\ \sin x\ dx$

1

-2

2

1

3

$\frac{2}{\pi}$

4

$\frac{4}{\pi}$

19

Multiple Choice

$20.\ \int_0^{\frac{\pi}{2}}\ \cos x\ dx$

1

-2

2

1

3

$\frac{2}{\pi}$

4

$\frac{4}{\pi}$

20

Multiple Choice

$22.\ \int_0^{\frac{\pi}{4}}\ \sec^2x\ dx$

1

-2

2

1

3

$\frac{2}{\pi}$

4

$\frac{4}{\pi}$

21

Finite Integral of Exponential and Logarithmic Functions

22

Multiple Choice

$21.\ \int_0^1\ e^x\ dx$

1

-2

2

e-1

3

$\frac{4}{\pi}$

23

Multiple Choice

$29.\ \int_1^e\ \frac{1}{x}\ dx$

1

-2

2

e-1

3

1

6.3 Definite Integrals and
Anti-derivatives

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