Integrate using u sub and trig sine and cosine

The video tutorial explains the process of U substitution in integration. It begins with an introduction to the concept, followed by identifying functions suitable for U substitution. The tutorial then details the integration process, including evaluating the integral with specific values. Finally, it concludes with the final calculation and result of the integral.

What is the primary purpose of using U-substitution in integration?

• To differentiate complex functions

• To simplify the integration of complex functions

• To find the limit of a function

• To solve algebraic equations

In the context of U-substitution, what is typically chosen as 'U'?

• The constant term in the function

• The most complex part of the function

• The derivative of the function

• The entire function

When applying U-substitution, what is the derivative of U with respect to x if U = sin(x)?

• cos(x)

• tan(x)

• sin(x)

• sec(x)

What is the integral of e^U with respect to U?

• e^U + C

• U^2/2 + C

• Ue^U + C

• e^(U^2) + C

What is the result of evaluating the integral from π/2 to 0 for e^(sin(x))?

• 1 + e

• 1 - e

• e + 1

• e - 1