Q. 72 - Calculus

Question

Use the Fundamental Theorem of Calculus to give alternative proofs of the integration facts shown in Exercises 72–76. You may assume that all functions here are integrable 

${\int }_a^{b}cdx=c(b-a)$

Step-by-Step Solution

Answer

Proved that ${\int }_a^{b}cdx=c(b-a)$

Step 1. Given information

The given limit ${\int }_a^{b}cdx=c(b-a)$

Step 2. Prove that ∫ a b c d x = c ( b - a ) using the fundamental theorem of calculas

$$\begin{gathered} {\int }_a^{b}cdx=c {\left[x\right]}_a^b \\ =c(b-a) [u\sin g Fundamental Theorem] \\ =c(b-a) \end{gathered}$$

Therefore,it is proved that ${\int }_a^{b}cdx=c(b-a)$