Understanding Trigonometric Integral Formulas

This video tutorial covers the six basic trigonometric integral formulas, focusing on the derivation of formulas for tangent, cotangent, secant, and cosecant integrals. It reviews the log rule for integration and demonstrates how natural logarithms appear in these integrals. The video provides step-by-step derivations using u substitution and multiplication tricks, offering insights into the mathematical processes behind these integral formulas.

Which trigonometric functions are missing integral formulas in the initial discussion?

• Secant and Cosecant

• Tangent and Cotangent

• Sine and Cosine

• Tangent, Cotangent, Secant, and Cosecant

What is the integral of 1/x dx equal to?

• ln|x| + C

• 1/x + C

• x^2/2 + C

• e^x + C

In the derivation of the integral of tangent, what substitution is made for u?

• u = sine x

• u = cosine x

• u = secant x

• u = tangent x

What is the antiderivative of 1/u in terms of natural logarithms?

• u^2/2

• 1/u

• ln|u|

• e^u

How is cotangent x expressed in terms of sine and cosine?

• sine x / cosine x

• 1 / sine x

• cosine x / sine x

• 1 / cosine x

What is the first step in deriving the integral of secant x?

• Multiply by secant x plus tangent x over secant x plus tangent x

• Multiply by secant x

• Differentiate secant x

• Use u-substitution

What is the derivative of secant x?

• cosine x

• secant x tangent x

• tangent x

• sine x

What substitution is used in the derivation of the integral of cosecant x?

• u = cosecant x

• u = cosecant x plus cotangent x

• u = sine x

• u = cosine x

What is the integral of secant x dx expressed in terms of natural logarithms?

• ln|secant x|

• ln|secant x plus tangent x|

• ln|tangent x|

• ln|cosecant x|

What is the purpose of multiplying by secant x plus tangent x over itself in the derivation?

• To simplify the expression

• To change the variable

• To make the numerator match the differential

• To eliminate secant x