Q. 32 If 鈭�-23f(x)dx=4,鈭�-26f(x)dx=9... [FREE SOLUTION]

Chapter 4: Q. 32 (page 353)

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

Short Answer

Expert verified

If ${鈭�}_{- 2}^{3} f (x) d x = 4, {鈭�}_{- 2}^{6} f (x) d x = 9, {鈭�}_{- 2}^{3} g (x) d x = 2$ and ${鈭�}_{3}^{6} g (x) d x = 3$ , then the exact value of ${鈭�}_{3}^{6} (2 f (x) - g (x)) d x$ is, $7$ .

Step by step solution

Step 1. Given information

${鈭�}_{- 2}^{3} f (x) d x = 4, {鈭�}_{- 2}^{6} f (x) d x = 9, {鈭�}_{- 2}^{3} g (x) d x = 2, {鈭�}_{3}^{6} g (x) d x = 3$ .

${鈭�}_{3}^{6} (2 f (x) - g (x)) d x$ .

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

${鈭�}_{3}^{6} (2 f (x) - g (x)) d x = 2 {鈭�}_{3}^{6} f (x) d x - {鈭�}_{3}^{6} g (x) d x = 2 ({鈭�}_{- 2}^{6} f (x) d x - {鈭�}_{3}^{- 2} f (x) d x) - 3 = 2 (9 - 4) - 3 = 2 (5) - 3 = 10 - 3 = 7$

Therefore, the required value is, $7$ .

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

Short Answer

Step by step solution

Step 1. Given information

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

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Most popular questions from this chapter

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