Integration of Inverse Trigonometric Functions

This video tutorial covers the integration of inverse trigonometric functions, including arc sine, arc cosine, arc tangent, arc cotangent, arc secant, and arc cosecant. It provides formulas and examples for each function, demonstrating how to substitute variables and apply the integration formulas. The video also offers resources for further learning and a formula sheet for reference.

What is the integral of arcsine of a function U, where U is a function of X?

• U arcsine U - sqrt(1 - U^2) + C

• U arcsine U + sqrt(1 - U^2) + C

• U arccosine U + sqrt(1 - U^2) + C

• U arccosine U - sqrt(1 - U^2) + C

How does the integral of arccosine differ from that of arcsine?

• It uses a square root instead of a natural log.

• It has a minus sign instead of a plus.

• It has a plus sign instead of a minus.

• It uses a natural log instead of a square root.

What is the integral of arctangent U?

• U arctangent U - sqrt(1 - U^2) + C

• U arctangent U + ln(sqrt(1 + U^2)) + C

• U arctangent U + sqrt(1 - U^2) + C

• U arctangent U - ln(sqrt(1 + U^2)) + C

Tags

CCSS.HSF.TF.B.7

Which function uses a natural log in its integration formula instead of a square root?

• Arcsine

• Arccosine

• Arctangent

• Arcsecant

In the example of integrating arctangent, what is the expression for U?

• 4X

• 3X + 5

• 5X^2

• X^2 + 5

Tags

CCSS.HSF.TF.B.7

What is the integral of arcsecant U?

• U arcsecant U - sqrt(U^2 - 1) + C

• U arcsecant U + sqrt(U^2 - 1) + C

• U arcsecant U - ln|U + sqrt(U^2 - 1)| + C

• U arcsecant U + ln|U + sqrt(U^2 - 1)| + C

How does the integral of arccosecant differ from that of arcsecant?

• It has a plus sign instead of a minus.

• It has a minus sign instead of a plus.

• It uses a square root instead of a natural log.

• It uses a natural log instead of a square root.

Tags

CCSS.HSF.TF.C.8

What is the expression for U in the arcsecant example?

• 5X^2

• 3X + 5

• X^2 + 5

• 4X

What is the general pattern observed in the integration formulas for inverse trigonometric functions?

• They all use a square root.

• They all use a natural log.

• They all have a similar structure with slight variations.

• They all have the same sign.

Where can you find more resources on calculus as mentioned in the video?

• On a different YouTube channel.

• In the video description.

• In the video comments.

• On the teacher's website.