Intro to Integration Review

your aunt derivative

indefinite integral

definite integral

derivative

calculating the area under a curve

 $\int_a^b\ f\left(x\right)\ dx=F\left(b\right)-F\left(a\right)$ 

integrating a function, with no +C

using rectangles to approximate the area under a curve

we didn't learn this!

positive

negative

zero

positive

negative

zero

positive

negative

zero

 $x^{\frac{1}{2}}+c$  

 $\frac{1}{2}x^{-\frac{1}{2}}+\ c$  

 $\frac{2}{3}x^{\frac{3}{2}}+\ c$  

 $\frac{3}{2}x^{\frac{3}{2}}+\ c$  

 $-2x^{-4}+C$  

 $4x^{-3}+C$  

 $\frac{8}{-3}x^{-2}$  

 $-4x^{-2}+C$  

 $\ln\left|x\right|-x+C$  

 $\frac{x^{-2}}{-2}-x+C$  

 $\ln\left|x\right|-1+C$  

 $1-x+C$  

 $=\tan x+c$  

 $=-\cos x+c$  

 $=-\sec x+c$  

 $=\operatorname{cosec}\ x\ +c$  

 $-19$  

 $41$  

 $-11$  

 $19$