Q. 39 If 鈭�-23f(x)dx=4,鈭�-26f(x)dx=9... [FREE SOLUTION]

Chapter 4: Q. 39 (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.
${鈭�}_{3}^{- 2} (2 x^{2} - 3 g (x)) d x$ .

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 ${鈭�}_{3}^{- 2} (2 x^{2} - 3 g (x)) d x$ is, $- \frac{52}{3}$ .

Step by step solution

Step 1. Given information

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

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

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

${鈭�}_{3}^{- 2} (2 x^{2} - 3 g (x)) d x = 2 {鈭�}_{3}^{- 2} x^{2} d x - 3 {鈭�}_{3}^{- 2} g (x) d x = 2 [\frac{1}{3} (- 2^{3} - 3^{3})] + 3 {鈭�}_{- 2}^{3} g (x) d x = 2 [\frac{1}{3} (- 8 - 27)] + 3 (2) = \frac{2 (35)}{3} + 6 = \frac{- 70 + 18}{3} = - \frac{52}{3}$

Therefore, the exact value is, $- \frac{52}{3}$ .

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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�3-22x2-3g(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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Recommended explanations on Math Textbooks

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