What is the general formula for integration?
∫ sin x dx = – cos x + C. ∫ cos x dx = sin x + C. ∫ sec2x dx = tan x + C. ∫ csc2x dx = – cot x + C.
What are the properties of integration?
Properties of Definite Integrals
| Properties | Description |
|---|---|
| Property 1 | ∫kj f(x)dx = ∫kj f(t)dt |
| Property 2 | ∫kj f(x)g(x)=-∫kj f(x)g(x),Also,∫jk f(x)g(x) = 0 |
| Property 3 | ∫kj f(x)g(x)=-∫lj f(x)g(x),Also,∫kl f(x)g(x) = 0 |
| Property 4 | ∫kj f(x)g(x)=∫kj f(j+k-x)g(x) |
What are the rules for integration of trigonometric integrals?
It is assumed that you are familiar with the following rules of differentiation. These lead directly to the following indefinite integrals. 1.) 2.) 3.) 4.) 5.) 6.) The next four indefinite integrals result from trig identities and u-substitution.
When do you use trigonometric substitutions in integration?
After we use these substitutions we’ll get an integral that is “do-able”. Take note that we are not integrating trigonometric expressions (like we did earlier in Integration: The Basic Trigonometric Forms and Integrating Other Trigonometric Forms and Integrating Inverse Trigonometric Forms.
How to substitute a tangent for a trig function?
However, the exponent on the tangent is odd and we’ve got a secant in the integral and so we will be able to use the substitution u = sec x u = sec x. This means stripping out a single tangent (along with a secant) and converting the remaining tangents to secants using (4) (4).
Which is the best way to integrate functions?
PROBLEM 1 : Integrate . Click HERE to see a detailed solution to problem 1. PROBLEM 2 : Integrate . Click HERE to see a detailed solution to problem 2. PROBLEM 3 : Integrate . Click HERE to see a detailed solution to problem 3. PROBLEM 4 : Integrate . Click HERE to see a detailed solution to problem 4.