Unit 6 Math Test: Units 6.7-6.10

What to do with 6^x

1.) 1/ln6 x 6^x

Reverse derivative for sinx

-cosx

How to integrate using substitution

1.) Check for any u values that would create a trig equation 2.) Substitute U in the best spot 3.) Find dU and then dX 4.) Multiply U equation by dX 5.) Simplify based on if du is divided or multiplied 6.) Take reverse derivative and add C

Process to solving definite integrals

1.) Find f(x) equation by using reverse process 2.) Substitute Higher X and subtract by Subsituted lower X

Find the function that satisfies the given conditions

1.) Find f(x) value 2.) Find C value that makes equation true

Solving definitive integrals using substitution

1.) Find where to put your U, scan for trig formulas 2.) Simplify based on division/multiplication of du 3.) Take reverse derivative 4.) Plug in your factors of the integral and subtract like normal

Finding value given a f(x) value

1.) Find your f(x) value 2.) Add your given value to the integral

How to find indefinite integrals

1.) Simplify equation 2.) Find your f(x) value 3.) Add C to the end of the equation 4.) Apply special rules

What to do once you obtain a trig formula

1.) Substitute u to form the equation 2.) Still multiply by your dX 3.) Final answer is trig symbol multiplied by remaining elements

Process of the integration

1.) You will need a trig formula, decide which one will be used 2.) Take the equation on the bottom and complete the square so you are left with a squared equation 3.) Change into trig format and add C

What to do with 2/x

2ln{x}

What to do with every indefinite integral

Add C to the end of the equation

Topic 6.8

Indefinite integrals

Topic 6.9

Integrating using substitution

Topic 6.10

Integrating with long division and completing the square

Topic 6.7

Solving definite integrals

Reverse derivative for csc^2x

cotx

Reverse derivative for cscxcotx

cscx

Reverse derivative of e^2

e^2x

1/[x]{x^2-1}

sec-1x

1/{1-x^2}

sin-1x

tanx

sinx/cosx

1/1 + u^2

tan-1x

What is 1/1 + x^2 equal to

tan^-1x

Reverse derivative for sec^2x

tanx