Question

Explain why ${\left[g\left(x\right)\right]}_a^b-{\left[h\left(x\right)\right]}_a^b={\left[g\left(x\right)-h\left(x\right)\right]}_a^b$this equation have to do with calculations of definite integrals with integration by parts?

Short answer

Difference between definite integral of two functions is equal to definite integration of difference between two functions.

Step-by-step solution

Step 1. Given information

${\left[g\left(x\right)\right]}_a^b-{\left[h\left(x\right)\right]}_a^b={\left[g\left(x\right)-h\left(x\right)\right]}_a^b$

Step 2. Explanation

It's given that ${\left[g\left(x\right)\right]}_a^b-{\left[h\left(x\right)\right]}_a^b={\left[g\left(x\right)-h\left(x\right)\right]}_a^b$

This is true as difference between definite integral of two functions is equal to definite integration of difference between two functions.