Inverse Trigonometric Functions Integration

This video tutorial introduces integration involving inverse trigonometric functions, focusing on pattern recognition to apply integration rules. It covers the formulas for arc sine, arc tangent, and arc secant, explaining why these are preferred over arc cosine, arc cotangent, and arc cosecant in integration. The tutorial provides three examples, demonstrating step-by-step integration using the respective formulas for arc sine, arc tangent, and arc secant, emphasizing the importance of identifying the correct pattern and determining the values of 'a' and 'u' for successful integration.

What is the key skill emphasized for applying integration rules effectively?

• Pattern recognition

• Memorization

• Speed

• Creativity

Tags

CCSS.HSF.TF.C.8

Which inverse trigonometric function is used when there is no square root in the denominator?

• Arc cosine

• Arc sine

• Arc tangent

• Arc secant

Tags

CCSS.HSF.TF.B.7

Why are arc cosine, arc cotangent, and arc cosecant not typically used in integration?

• They are too complex

• They are the opposites of more commonly used functions

• They are not inverse functions

• They do not have integration formulas

Tags

CCSS.HSF.TF.B.7

In the arc sine integration example, what is the value of 'a' when the denominator is the square root of 16 minus x squared?

• 2

• 3

• 5

• 4

Tags

CCSS.HSF.TF.B.7

What is the anti-derivative of the function with a denominator of a squared plus u squared?

• Arc cosine

• Arc sine

• Arc tangent

• Arc secant

In the arc tangent example, what is the value of 'u' if u squared equals 16x squared?

• 3x

• 4x

• 2x

• 5x

Tags

CCSS.HSF.TF.A.4

What adjustment is made in the arc secant example to fit the pattern?

• Divide the denominator by 2

• Divide the denominator by 3

• Multiply the numerator by 3

• Multiply the numerator by 2

Tags

CCSS.HSF.TF.B.7

In the arc secant example, what is the value of 'a' when a squared equals 4?

• 1

• 3

• 2

• 4

Tags

CCSS.HSF.TF.B.7

What is the anti-derivative formula used for the arc secant example?

• 1/a times arc sine

• 1/a times arc secant

• 1/a times arc cosine

• 1/a times arc tangent

What is the final step in finding the anti-derivative in the arc secant example?

• Multiply by a constant C

• Add a constant C

• Divide by a constant C

• Subtract a constant C