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Evaluate the integral. S. sec Sx dx sec 8x tan 8x - In|sec Sx + tan Sx| + C 1 sec 8x tan 8x + In|sec 8x + tan Sx| + C .O 16 16 sec 8x tan 8x+ 16 16 *C + C sec 28x tan 8x +In|sec 8x + tan Sx| + C 16

Evaluate the integral. S. sec Sx dx sec 8x tan 8x - In|sec Sx + tan Sx| + C 1 sec 8x tan 8x + In|sec 8x + tan Sx| + C .O 16 16 sec 8x tan 8x+ 16 16 *C + C sec 28x tan 8x +In|sec 8x + tan Sx| + C 16

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter8: Further Techniques And Applications Of Integration
Section8.CR: Chapter 8 Review
Problem 11CR
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**Evaluate the integral.** \[ \int \sec^3 8x \, dx \] **Options provided:** 1. \(\frac{1}{2} \sec 8x \tan 8x - \frac{1}{2} \ln |\sec 8x + \tan 8x| + C\) 2. \(\frac{1}{16} \sec 8x \tan 8x + \frac{1}{16} \ln |\sec 8x + \tan 8x| + C\) 3. \(\frac{1}{16} \sec 8x \tan 8x + \frac{x}{16} + C\) 4. \(\frac{1}{16} \sec^2 8x \tan 8x + \frac{1}{16} \ln |\sec 8x + \tan 8x| + C\) Please select the correct evaluation from the options provided. **Explanation:** - The integral given involves the secant function raised to the third power, multiplied by 8x, and integrated with respect to \( x \). - Evaluating such integrals typically involves using specific integral formulas and trigonometric identities. - Each option provided gives a potential form of the evaluated integral with a constant of integration \( C \), which is common in indefinite integrals. **Steps that might be involved in solving:** 1. Break down the integral into simpler parts if possible. 2. Use substitution methods if an integral seems too complex. 3. Apply known integral formulas relevant to \(\sec\) and \(\tan\) functions. 4. Simplify using logarithmic identities and constants are then combined. **Note:** The correct evaluation will depend on the proper application of trigonometric integral identities and constant adjustments.
Transcribed Image Text:**Evaluate the integral.** \[ \int \sec^3 8x \, dx \] **Options provided:** 1. \(\frac{1}{2} \sec 8x \tan 8x - \frac{1}{2} \ln |\sec 8x + \tan 8x| + C\) 2. \(\frac{1}{16} \sec 8x \tan 8x + \frac{1}{16} \ln |\sec 8x + \tan 8x| + C\) 3. \(\frac{1}{16} \sec 8x \tan 8x + \frac{x}{16} + C\) 4. \(\frac{1}{16} \sec^2 8x \tan 8x + \frac{1}{16} \ln |\sec 8x + \tan 8x| + C\) Please select the correct evaluation from the options provided. **Explanation:** - The integral given involves the secant function raised to the third power, multiplied by 8x, and integrated with respect to \( x \). - Evaluating such integrals typically involves using specific integral formulas and trigonometric identities. - Each option provided gives a potential form of the evaluated integral with a constant of integration \( C \), which is common in indefinite integrals. **Steps that might be involved in solving:** 1. Break down the integral into simpler parts if possible. 2. Use substitution methods if an integral seems too complex. 3. Apply known integral formulas relevant to \(\sec\) and \(\tan\) functions. 4. Simplify using logarithmic identities and constants are then combined. **Note:** The correct evaluation will depend on the proper application of trigonometric integral identities and constant adjustments.
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ISBN:
9780321964038
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Publisher:
Pearson Addison Wesley,
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