Chapter 4: Q. 29 (page 353)

If $\int_{- 2}^{3} f (x) d x = 4, \int_{- 2}^{6} f (x) d x = 9, \int_{- 2}^{3} g (x) d x = 2$ and $\int_{3}^{6} g (x) d x = 3$ ,then find the values of each definite integral in Exercises $29 - 40$ . If there is not enough information, explain why.
$\int_{3}^{6} f (x) d x$ .

Short Answer

Expert verified

If $\int_{- 2}^{3} f (x) d x = 4, \int_{- 2}^{6} f (x) d x = 9, \int_{- 2}^{3} g (x) d x = 2$ and $\int_{3}^{6} g (x) d x = 3$ , then the value of $\int_{3}^{6} f (x) d x$ is, $5$ .

Step by step solution

Step 1. Given information

$\int_{- 2}^{3} f (x) d x = 4, \int_{- 2}^{6} f (x) d x = 9, \int_{- 2}^{3} g (x) d x = 2, \int_{3}^{6} g (x) d x = 3$ .

$\int_{3}^{6} f (x) d x$ .

Step 2. The definite integral can be found out as,

$\int_{3}^{6} f (x) d x = \int_{- 2}^{6} f (x) d x - \int_{3}^{- 2} f (x) d x = 9 - 4 = 5$

Therefore, the required value is, $5$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

If $\int_{- 2}^{3} f (x) d x = 4, \int_{- 2}^{6} f (x) d x = 9, \int_{- 2}^{3} g (x) d x = 2$ and $\int_{3}^{6} g (x) d x = 3$ ,then find the values of each definite integral in Exercises $29 - 40$ . If there is not enough information, explain why.
$\int_{3}^{6} f (x) d x$ .

Short Answer

Step by step solution

Step 1. Given information

Step 2. The definite integral can be found out as,

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Geometry

Calculus

Theoretical and Mathematical Physics

Applied Mathematics

Decision Maths

Study anywhere. Anytime. Across all devices.

If ∫-23f(x)dx=4,∫-26f(x)dx=9,∫-23g(x)dx=2and ∫36g(x)dx=3,then find the values of each definite integral in Exercises 29-40. If there is not enough information, explain why.∫36fxdx.

Short Answer

Step by step solution

Step 1. Given information

Step 2. The definite integral can be found out as,

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Geometry

Calculus

Theoretical and Mathematical Physics

Applied Mathematics

Decision Maths

Study anywhere. Anytime. Across all devices.

If $\int_{- 2}^{3} f (x) d x = 4, \int_{- 2}^{6} f (x) d x = 9, \int_{- 2}^{3} g (x) d x = 2$ and $\int_{3}^{6} g (x) d x = 3$ ,then find the values of each definite integral in Exercises $29 - 40$ . If there is not enough information, explain why.
$\int_{3}^{6} f (x) d x$ .