Integral Calculus Techniques and Concepts

Integral Calculus Techniques and Concepts

Assessment

Interactive Video

Mathematics

11th - 12th Grade

Practice Problem

Hard

Created by

Thomas White

FREE Resource

The video tutorial covers solving an integral involving fractional and integer exponents. The instructor discusses the challenges of factoring and setting up a U-substitution. A strategy is developed to factor the terms and simplify the integral using U-substitution. The solution involves using the arc sine function to solve the integral. The tutorial concludes with final thoughts on the problem-solving process.

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8 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the initial integral problem discussed in the video?

Integral of dx over the square root of x^4 + x

Integral of dx over the square root of x^4 + x^2

Integral of dx over the square root of x^4 - x

Integral of dx over the square root of x^4 - x^2

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Why is factoring out a fractional exponent challenging?

It results in a complex polynomial.

It leads to another fractional exponent.

It simplifies the equation too much.

It makes the integral unsolvable.

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the benefit of the chosen factoring method?

It removes the need for substitution.

It aligns the exponents for easier substitution.

It simplifies the integral to a linear form.

It eliminates all exponents.

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the initial attempt for u-substitution?

Using x^3 as U.

Using the entire expression as U.

Using x^2 as U.

Using x^5 as U.

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the final choice for U in the substitution?

x^(4/7)

x^(2/7)

x^(5/7)

x^(3/7)

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the derivative of the chosen U?

3/7 x^(2/7)

3/7 x^(-2/7)

5/7 x^(-2/7)

5/7 x^(2/7)

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the final form of the integral after substitution?

Arc tangent of U

Arc cosine of U

Arc sine of U

Arc cotangent of U

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