Chapter 14: Q 3 (page 1131)

Express $\int_{a}^{b} f (x) d x$ in terms of something on the boundary of $[a, b]$ .

Short Answer

Expert verified

The required value is :-

$\int_{a}^{b} f (x) d x = F (b) - F (a)$ , where $F$ is integral of $f$ .

Step by step solution

Step 1. Given Information

We have to find the value of the integral $\int_{a}^{b} f (x) d x$ in terms of boundary of $[a, b]$

Step 2. Required solution

Let the integral of function $f (x)$ is $F (x)$ .

Then we have :-

$\int_{a}^{b} f (x) d x = F (x)]_{a}^{b}$

Then put the limits, then we have :-

$\int_{a}^{b} f (x) d x = F (b) - F (a)$

This is the required representation of the given integral in some boundary of $[a, b]$ .

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Express $\int_{a}^{b} f (x) d x$ in terms of something on the boundary of $[a, b]$ .

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Required solution

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Express $\int_{a}^{b} f (x) d x$ in terms of something on the boundary of $[a, b]$ .