Integration by parts Problem No 1 - Integration - Diploma Maths - 2

TL;DR

Learn how to solve the integral of X*sin(2X) using the integration by parts method.

Transcript

click the bell icon to get latest videos from equator arrow friends in this video we are going to see a new form of integration that is integration by parts let us see by starting problem number by we have integral X into sine 2x DX now how to identify this type that is a question integration by parts means whenever we have two functions in product... Read More

Key Insights

• 🥳 Integration by parts is used to solve integrals of functions in product form.
• 🇧🇻 The indigo UV rule helps determine which function is "U" and which is "V".
• 🪈 Rearranging the functions may be necessary to match the order in the indigo UV rule.

Questions & Answers

Q: How is integration by parts used to solve the integral of X*sin(2X)?

Integration by parts involves identifying the functions in product form and applying the integral UV rule. In this case, X is designated as "U" and sin(2X) is designated as "V". The integral of Xsin(2X) is then expressed as Uintegral(V) - integral(U*dV).

Q: What are the categories of functions used in the indigo UV rule?

The indigo UV rule categorizes functions into four types: inverse functions (such as sine inverse, cos inverse), algebraic functions (without sine, cos, log), trigonometric functions (with sine, cos, tan), and exponential functions (with X as the power).

Q: How should the functions be arranged if they are in a different order?

If the given problem is written as sine(2X)X, the functions must be rearranged to match the order of the indigo UV rule. In this case, it would be Xsin(2X).

Q: What is the next step after designating the functions as "U" and "V"?

After designating the functions, take the derivative of "U" and integrate "V" to obtain U*integral(V). Then, take the integral of "U" multiplied by the derivative of "V". Substituting these values into the integral UV rule will yield the solution.

Summary & Key Takeaways

• Integration by parts is a method used to integrate functions that are in product form.

• The indigo UV rule is used to determine which function should be designated as "U" and which should be designated as "V".

• In this video, the problem of integrating X*sin(2X) is solved using the integration by parts method.