Integration Formulas for Trigonometric Functions

This video tutorial provides a comprehensive list of integration formulas for common trigonometric functions, including sine, cosine, tangent, cotangent, secant, and cosecant. It covers the indefinite integrals of these functions, explains the use of natural logarithms in some cases, and introduces reduction formulas for higher power functions. The video also offers downloadable formula sheets for further study.

What is the indefinite integral of sin(x)?

• -sin(x) + C

• sin(x) + C

• -cos(x) + C

• cos(x) + C

How is the indefinite integral of cos(ax + b) expressed?

• -1/a sin(ax + b) + C

• sin(ax + b) + C

• -sin(ax + b) + C

• 1/a sin(ax + b) + C

What is the indefinite integral of tan(x)?

• ln|cot(x)| + C

• ln|sec(x)| + C

• ln|sin(x)| + C

• ln|cos(x)| + C

Tags

CCSS.HSF.TF.A.2

Which function is the reciprocal of cosine?

• Cosecant

• Secant

• Tangent

• Cotangent

What is the indefinite integral of sin^2(x)?

• 12x + sin(x)cos(x) + C

• 12x - 4sin(2x) + C

• 12x + 4sin(2x) + C

• 12x - sin(x)cos(x) + C

Tags

CCSS.HSF.TF.C.9

What is the double angle formula for sin(2x)?

• 1 - 2sin^2(x)

• 2sin(x)cos(x)

• sin^2(x) - cos^2(x)

• 2cos^2(x) - 1

What is the reduction formula for the integral of sin^n(x)?

• -1/n sin^(n-1)(x)cos(x) + (n-1)/n integral of sin^(n-2)(x) dx

• 1/n sin^(n-1)(x)cos(x) + (n-1)/n integral of sin^(n-2)(x) dx

• 1/n sin^(n-1)(x)cos(x) - (n-1)/n integral of sin^(n-2)(x) dx

• -1/n sin^(n-1)(x)cos(x) - (n-1)/n integral of sin^(n-2)(x) dx

What is the integration by parts formula?

• Integral of u dv = uv - integral of v du

• Integral of u dv = uv + integral of v du

• Integral of u dv = vu + integral of u dv

• Integral of u dv = vu - integral of u dv

What is the reduction formula for the integral of cos^n(x)?

• -1/n cos^(n-1)(x)sin(x) + (n-1)/n integral of cos^(n-2)(x) dx

• -1/n cos^(n-1)(x)sin(x) - (n-1)/n integral of cos^(n-2)(x) dx

• 1/n cos^(n-1)(x)sin(x) - (n-1)/n integral of cos^(n-2)(x) dx

• 1/n cos^(n-1)(x)sin(x) + (n-1)/n integral of cos^(n-2)(x) dx

What is the integral of tan^n(x) when n is not equal to 1?

• 1/(n+1) tan^(n+1)(x) + integral of tan^(n+2)(x) dx

• 1/(n-1) tan^(n-1)(x) - integral of tan^(n-2)(x) dx

• 1/(n+1) tan^(n+1)(x) - integral of tan^(n+2)(x) dx

• 1/(n-1) tan^(n-1)(x) + integral of tan^(n-2)(x) dx