Antiderivatives & Differential Equations

 $\int_{ }^{ }\sec^2xdx=?$  

•  $\frac{\sec^3x}{3}+c$  

•  $\sec x+c$  

•  $\tan x+c$  

•  $\sec x\tan x+c$  

 $\int_{ }^{ }\tan x\cot xdx$  

•  $\csc x+c$  

•  $\tan^2x\cot^2x+c$  

•  $\sec x+c$  

•  $x+c$  

 $\int\frac{1}{\csc x}dx$  

•  $-\cos x+c$  

•  $\sin x+c$  

•  $\cot^2x+c$  

•  $\sec x+c$  

If $\frac{dy}{dx}=4x-1$ and  $y\left(1\right)=3$  , then  $y$  equals 

•  $2x^2-x$  

•  $2x^2-x+2$  

•  $2x^2-x+1$  

•  $2x^2+1$  

A stone is thrown straight up from the top of a building with initial velocity $40\ \frac{ft}{\sec}$  and hits the ground 4 sec later (s(4)=0). What is the height of the building, in feet?

(The constant acceleration is approximately g= $32\ \frac{ft}{\sec^2}$ ) 

• 88

• 96

• 112

• 128