Problem : Given that exdx = e2 - and exdx = 1 - , find exdx.

By telescoping limits, we have

exdx + exdx = exdx    

so

exdx = e2 - - 1 - = e2 - 1.    

Problem : If xdx = 3/2, x2dx = 7/3, and (x2 + 2x)dx = 180/3, find (x2 + 2x)dx.

Here we use all three properties introduced in this section:


x2 + 2xdx=x2dx + 2xdx + x2 + 2xdx  
 = +2 +  
 =  

Problem : Compute + 3dx using elementary geometry.

We have


+ 3dx=dx + 3dx  
 = + 6  

since the two integrals correspond respectively to a semicircle of radius 1 and a rectangle with height 3 and width 2.