Calculus II : Integration By Parts (Level 5 of 6)

The video tutorial covers the application of integration by parts to solve definite integrals. It begins with a brief overview of the technique and its relation to the fundamental theorem of calculus. Three examples are provided: integrating X times sin(3X), X times 5^X, and (X^2 + 1) times e^(-X). The tutorial demonstrates step-by-step solutions, including the use of the tabular method for more complex integrals.

What is the main difference between definite and indefinite integrals as discussed in the video?

• Definite integrals do not require a function.

• Indefinite integrals are always zero.

• Indefinite integrals are evaluated from A to B.

• Definite integrals have limits of integration.

In the first example, what is chosen as the function 'u' for integration by parts?

• cos(3x)

• sin(3x)

• 3x

• x

What is the integral of sin(3x) dx as used in the first example?

• -1/3 cos(3x)

• 3 cos(3x)

• 1/3 cos(3x)

• -3 cos(3x)

In the second example, what is the integral of 5^x dx?

• ln(5) * 5^x

• 5^x * ln(5)

• ln(5) / 5^x

• 5^x / ln(5)

What method is used in the final example to handle the integration by parts?

• Trigonometric substitution

• Substitution method

• Tabular method

• Partial fraction decomposition

In the final example, what is the function 'u' chosen for the tabular method?

• e^(-x)

• x^2 + 1

• x

• ln(x)

What is the final form of the definite integral in the last example?

• 6/e - 3

• -6/e + 3

• 3/e + 6

• -3/e + 6