Chapter 4: Q. 31 (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.
$\int_{- 2}^{6} (f (x) + g (x)) d x$ .

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 exact value of $\int_{- 2}^{6} (f (x) + g (x)) d x$ is, $14$ .

Step by step solution

Step 1. Given information

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

$\int_{- 2}^{6} (f (x) + g (x)) d x$ .

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

$\int_{- 2}^{6} (f (x) + g (x)) d x = \int_{- 2}^{6} f (x) d x + \int_{- 2}^{6} g (x) d x = 9 + \int_{- 2}^{3} g (x) d x + \int_{3}^{6} g (x) d x = 9 + 2 + 3 = 14$

Therefore, the required value is, $14$ .

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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.
$\int_{- 2}^{6} (f (x) + g (x)) d x$ .

Short Answer

Step by step solution

Step 1. Given information

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

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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.∫-26(f(x)+g(x))dx.

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

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Applied Mathematics

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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.
$\int_{- 2}^{6} (f (x) + g (x)) d x$ .