Q. 42 Use the Fundamental Theorem of C... [FREE SOLUTION]

Chapter 4: Q. 42 (page 373)

Use the Fundamental Theorem of Calculus to find the exact values of the given definite integrals. Use a graph to check your answer.
${鈭�}_{鈭� 3}^{2} 鈥� \frac{x^{2} + 5}{2 x} d x$

Short Answer

Expert verified

Ans: The exact value of, ${鈭�}_{鈭� 3}^{2} 鈥� \frac{x^{2} + 5}{2 x} d x = \frac{5 (2 (\ln 鈦� (2) + \ln 鈦� (鈭� 1)) 鈭� 2 \ln 鈦� (鈭� 3) 鈭� 1)}{4}$

Step by step solution

Step 1. Given information.

given expression,

${鈭�}_{鈭� 3}^{2} 鈥� \frac{x^{2} + 5}{2 x} d x$

Step 2. The objective is to determine the exact value of the definite integral.

The exact value is calculated as shown below,

${鈭�}_{鈭� 3}^{2} 鈥� \frac{x^{2} + 5}{2 x} d x = \frac{1}{2} {鈭�}_{鈭� 3}^{2} 鈥� x d x + \frac{5}{2} {鈭�}_{鈭� 3}^{2} 鈥� \frac{1}{x} d x = [\frac{x^{2}}{4} + \frac{5 \ln (x)}{2}]_{鈭� 3}^{2} = [\frac{5 \ln 鈦� (| x |) + \frac{x^{2}}{2}}{2}]_{鈭� 3}^{2} = \frac{5 \ln 鈦� (2) + 5 \ln 鈦� (鈭� 1) 鈭� 5 \ln 鈦� (鈭� 3) 鈭� \frac{5}{2}}{2} = \frac{5 (2 (\ln 鈦� (2) + \ln 鈦� (鈭� 1)) 鈭� 2 \ln 鈦� (鈭� 3) 鈭� 1)}{4}$

Therefore, the exact value is $\frac{5 (2 (\ln 鈦� (2) + \ln 鈦� (鈭� 1)) 鈭� 2 \ln 鈦� (鈭� 3) 鈭� 1)}{4}$

Step 3. Check:

The required graph is,

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Use the Fundamental Theorem of Calculus to find the exact values of the given definite integrals. Use a graph to check your answer.
${鈭�}_{鈭� 3}^{2} 鈥� \frac{x^{2} + 5}{2 x} d x$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. The objective is to determine the exact value of the definite integral.

Step 3. Check:

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Use the Fundamental Theorem of Calculus to find the exact values of the given definite integrals. Use a graph to check your answer. 鈭�鈭�32鈥�x2+52xdx

Short Answer

Step by step solution

Step 1. Given information.

Step 2. The objective is to determine the exact value of the definite integral.

Step 3. Check:

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Mechanics Maths

Decision Maths

Probability and Statistics

Pure Maths

Statistics

Study anywhere. Anytime. Across all devices.

Use the Fundamental Theorem of Calculus to find the exact values of the given definite integrals. Use a graph to check your answer.
${鈭�}_{鈭� 3}^{2} 鈥� \frac{x^{2} + 5}{2 x} d x$