Chapter 4: Q. 8 (page 351)

Draw pictures illustrating the fact that if $a \leq c \leq b$ then
$\int_{a}^{c} f (x) d x + \int_{c}^{b} f (x) d x = \int_{a}^{b} f (x) d x$

Short Answer

Expert verified

The graphs are as follows

Step by step solution

Step 1. Given information

An identity is given as $\int_{a}^{c} f (x) d x + \int_{c}^{b} f (x) d x = \int_{a}^{b} f (x) d x$

Step 2. Graphs

Draw the of individual functions and then compare them.

The first graph of $f (x) = x^{2} & f r o m 0 \to 0.5$

Now the second graph of $f (x) = x^{2} & f r o m 0.5 \to 1$

Last graph of $f (x) = x^{2} & f r o m 0 \to 1$

From the above graphs we can conclude that

$\int_{a}^{c} f (x) d x + \int_{c}^{b} f (x) d x = \int_{a}^{b} f (x) d x$

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Draw pictures illustrating the fact that if $a \leq c \leq b$ then
$\int_{a}^{c} f (x) d x + \int_{c}^{b} f (x) d x = \int_{a}^{b} f (x) d x$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Graphs

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Draw pictures illustrating the fact that if a≤c≤bthen∫acf(x)dx+∫cbf(x)dx=∫abf(x)dx

Short Answer

Step by step solution

Step 1. Given information

Step 2. Graphs

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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Draw pictures illustrating the fact that if $a \leq c \leq b$ then
$\int_{a}^{c} f (x) d x + \int_{c}^{b} f (x) d x = \int_{a}^{b} f (x) d x$