Calculus Derivatives and Integrals

Calculus Derivatives and Integrals

Assessment

Interactive Video

Mathematics

9th - 10th Grade

Practice Problem

Hard

Created by

Thomas White

FREE Resource

The video tutorial covers integration techniques for composite, power, trigonometric, and product functions. It explains the use of the chain rule and the importance of adjusting factors to achieve correct integration results. The tutorial provides step-by-step examples to illustrate each concept, ensuring a comprehensive understanding of integration in calculus.

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13 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the integral of cosine of 6X?

cos(6X) + C

sin(6X) + C

1/6 sin(6X) + C

6 sin(6X) + C

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which rule is applied to find the derivative of s(6X)?

Quotient Rule

Power Rule

Product Rule

Chain Rule

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Why do we introduce a factor of 1/6 in the integral of cosine of 6X?

To eliminate the constant of integration

To make the integral easier to compute

To match the derivative with the original function

To simplify the expression

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the result of differentiating 1/6 sin(6X) + C?

cos(6X)

1/6 cos(6X)

6 cos(6X)

sin(6X)

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What happens to the power when integrating (3x + 2)^5?

It decreases by one

It remains the same

It doubles

It increases by one

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What factor is introduced to adjust the integral of (3x + 2)^5?

1/6

1/9

1/3

1/18

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the derivative of (3x + 2)^6?

18(3x + 2)^5

3(3x + 2)^5

6(3x + 2)^5

9(3x + 2)^5

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