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Chapter 6: Techniques of integration

Expert-verified
Essential Calculus: Early Transcendentals
Pages: 311 - 364
Essential Calculus: Early Transcendentals

Essential Calculus: Early Transcendentals

Book edition 2nd
Author(s) James Stewart
Pages 830 pages
ISBN 9781133112280

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Illustration

353 Questions for Chapter 6: Techniques of integration

  1. \(5 - 32\)Determine whether each integral is convergent or divergent. Evaluate those that are convergent.

    Found on Page 360

  2. Evaluate the Integral: \(\int\limits_0^\pi {{{\cos }^6}\theta } d\theta \)

    Found on Page 326

  3. Evaluate the integral\(\int_{\rm{0}}^{\rm{1}} {\frac{{\sqrt {{\rm{arctanx}}} }}{{{\rm{1 + }}{{\rm{x}}^{\rm{2}}}}}} {\rm{dx}}\)

    Found on Page 363

  4. Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.

    Found on Page 362

  5. Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpson's Rule to approximate the given integral with the specified value of\(n\). (Round your answers to six decimal places.)

    Found on Page 350

  6. Evaluate the integral:\(\int {\frac{y}{{(y + 4)(2y - 1)}}} dy\).

    Found on Page 334

  7. Evaluate the integral\(\int {{{\sin }^{ - 1}}\sqrt x .dx} \)

    Found on Page 340

  8. Evaluate the integral\(\int {{p^5}\ln pdp} \)

    Found on Page 316

  9. Evaluate the integral\(\int {y\sqrt {6 + 4y - 4{y^2}} } .dy\)\(\)

    Found on Page 340

  10. Evaluate the integral\(\int_{\rm{1}}^{\rm{2}} {\frac{{\sqrt {{{\rm{x}}^{\rm{2}}}{\rm{ - 1}}} }}{{\rm{x}}}} {\rm{dx}}\)

    Found on Page 363

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