Problem : Given that e ^{x} dx = e ^{2} - and e ^{x} dx = 1 - , find e ^{x} dx .
By telescoping limits, we have
e ^{x} dx + e ^{x} dx = e ^{x} dx |
e ^{x} dx = e ^{2} - - 1 - = e ^{2} - 1. |
Problem : If xdx = 3/2 , x ^{2} dx = 7/3 , and (x ^{2} + 2x)dx = 180/3 , find (x ^{2} + 2x)dx .
Here we use all three properties introduced in this section:
x ^{2} + 2xdx | = | x ^{2} dx + 2 xdx + x ^{2} + 2xdx | |
= | +2 + | ||
= |
Problem : Compute + 3 dx using elementary geometry.
We have
+ 3dx | = | dx + 3dx | |
= | + 6 |