Ch. 4 Sec 4,5,6 Flashcards
What is the second fundamental theorem of calculus
The derivative of the anti derivative from a to x of f of t dt equals f of x
Take derivative of anti derivative and it gets you back to the same function you started with
What is the fundamental theorem of calculus
Integral from a to b of f of x dx equals capital F of b - capital F of a
Capital F is the anti derivative of f
What do you do with the integral a to x
The function is the same except plug in x for the variable
What happens when it is a variable to a variables
No short cut
Integral of a to f(x)
Plug in upper limit then multiply by the derivative of the upper limit
General power rule
Differentiate quantities raised to a power
What to do for trig substitution
Let u equal the angle
What to do for too much variable on the outside
U substitution
Too much variable on the outside when need to integrate with numbers
Change the numbers so that they work with the u substitution
When integrating an odd function to the same number limit although neg and pos
= 0
Trapezoidal rule
B minus a over n times the quantity f of first number plus two times f of the other numbers plus f of the last number
Average value of a function
One over b minus a of the integral from a to b f of x dx
Anti derivative of
Cos x
Sin x
Anti derivative of sin x
-cos x
Anti derivative of
Sec^2 x
Tanx
