Integration Using Trigonometric Formulas Quiz

This video tutorial demonstrates how to integrate using the six basic trigonometric integral formulas. It covers two examples: integrating 2 times sine of 5x and x squared cotangent of x cubed. The video explains the use of u-substitution to simplify the integrals and apply the basic integral formulas. The first example involves rewriting the integral in terms of u and solving for dx, while the second example uses a similar approach to handle the cotangent function. The tutorial concludes with a brief mention of additional examples in a subsequent video.

What is the main topic of the video?

• Graphing trigonometric functions

• Solving algebraic equations

• Integration using six basic trigonometric integral formulas

• Differentiation using trigonometric formulas

In the first example, what substitution is made for u?

• u = 2x

• u = sin(x)

• u = 5x

• u = x^2

What is the differential du in terms of dx for the substitution u = 5x?

• du = 5dx

• du = dx/5

• du = 2dx

• du = dx/2

What is the result of integrating 2 times sine of 5x?

• -(2/5) cos(5x) + C

• (2/5) sin(5x) + C

• -(5/2) cos(5x) + C

• (5/2) sin(5x) + C

Which integral formula is applied after substitution in the first example?

• Integral of cotangent

• Integral of tangent

• Integral of sine

• Integral of cosine

In the second example, what substitution is made for u?

• u = sin(x)

• u = cot(x)

• u = x^2

• u = x^3

What is the differential du in terms of dx for the substitution u = x^3?

• du = x^2 dx

• du = 3x^2 dx

• du = 3x dx

• du = x dx

What is the result of integrating x squared cotangent x cubed?

• (1/3) ln|cos(x^3)| + C

• (3/1) ln|sin(x^3)| + C

• (1/3) ln|sin(x^3)| + C

• (3/1) ln|cos(x^3)| + C

What is the purpose of u-substitution in integration?

• To find the derivative

• To solve differential equations

• To simplify the integrand

• To change the variable of integration

Which integral formula is applied after substitution in the second example?

• Integral of cotangent

• Integral of tangent

• Integral of cosine

• Integral of sine