15 Methods of integration Flashcards
What are the methods of integration?
- Integration by inspection
- Integration by substitution
- Integration by parts
- reverse chain rule
- Partial fractions
How do you integrate something to the power of e?
-Derivative of the power and then divide by this.
How do you integrate using inspection?
-Use formula booklet
How do you use the reverse chain rule?
-Raise the power by 1, then divide the outside by the new power + derivative inside the bracket.
How do you do integration by parts?
- Give priority to x or lnx and make this u.
- Then make the other part of the function dv/dx
- Differentiate to get du/dx and integrate to get V
- Then put this into formula given.
How do you do integration by substitution?
- Step 1 change dx for something else
- Step 2 change limits as needed
- Step 3 change what is in brackets
How do you know what substitution to make in integration if not given one?
-Do whatever is inside a square root or bracket.
How do you know if trapezium rule has given overestimate or underestimate?
- If it is concave underestimate
- If it is convex over estimate.
How do you calculate % error?
-Difference/exact x 100
How can you estimate the value of an integral?
Using trapezium rule
How do you input trapezium rule into calculator?
1/2(h)(y0+yn+2( the rest of the ys)
