Integration Basic Rules

The integral is calculating

• "the slope of a tangent line"

• "the area under a curve"

• "the steepness of a space"

• "the length of a circle arc"

What's the resulting function of

  $\int dx$  ?

• d

• x

• x+c

• 1

The sign for integration represents letter S, as:

• Solution

• Sum

• Series

• Statement

Solve the integral

  $\int tdx$  

•  $\frac{t^2}{2}+c$  

•  $\frac{x^2}{2}+c$  

•  $tx+c$  

•  undefined

Why  $e^x$   was so lonely at the party?

• Because it has the greatest power.

• Because every time he tried to integrate, he ended up with himself.

• Because it has no function.

• Blah blah blah ...

What would be the best substitution to make, for solving the integral:  $\int\left(x^2+1\right)2xdx$  

•  $x^2+1=t$  

•  $x^2=t$  

•  $2x=t$  

•  $x=t$  

What would be the best substitution to make, for solving the integral:  $\int\left(\frac{\ln x}{x}\right)dx$  

•  $\frac{1}{x}=t$  

•  $x=t$  

•  $\ln x=t$  

•  $\frac{x}{x}=t$  

What would be the best substitution to make, for solving the integral:  $\int\left(\frac{\arctan x}{1+x^2}\right)dx$  

•  $1+x^2=t$  

•  $\arctan=t$  

•  $\tan x=t$  

•  $\arctan x=t$  

What would be the best substitution to make, for solving the integral:  $\int\left(\sin2x\right)dx$  

•  $\sin2x=t$  

•  $x=t$  

•  $\sin x=t$  

•  $\cos2x=t$  

What would be the best substitution to make, for solving the integral:  $\int\left(\frac{e^x}{1+e^{2x}}\right)dx$  

•  $e^{2x}=t$  

•  $e^x=t$  

•  $\frac{e^x}{1+e^{2x}}=t$  

•  $2x=t$