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5.7-bo'lim: Aniq integrallarni hisoblash

  1. Quyidagi integrallarning har birini baholang.
    1. \( \displaystyle \int{{\cos \left( x \right) - \frac{3}{{{x^5}}}\,dx}}\)
    2. \( \displaystyle \int_{{ - 3}}^{4}{{\cos \left( x \right) - \frac{3}{{{x^5}}}\,dx}}\)
    3. \( \displaystyle \int_{1}^{4}{{\cos \left( x \right) - \frac{3}{{{x^5}}}\,dx}}\)
    Yechim

Iloji bo'lsa, quyidagi integrallarning har birini baholang. Agar buning iloji bo'lmasa, nima uchun integralni baholash mumkin emasligini aniq tushuntiring.

  1. \( \displaystyle \int_{1}^{6}{{12{x^3} - 9{x^2} + 2\,dx}}\) Yechim
  2. \( \displaystyle \int_{{ - 2}}^{1}{{5{z^2} - 7z + 3\,dz}}\) Yechim
  3. \( \displaystyle \int_{3}^{0}{{15{w^4} - 13{w^2} + w\,dw}}\) Yechim
  4. \( \displaystyle \int_{1}^{4}{{\frac{8}{{\sqrt t }} - 12\sqrt {{t^3}} \,dt}}\) Yechim
  5. \( \displaystyle \int_{1}^{2}{{\frac{1}{{7z}} + \frac{{\sqrt[3]{{{z^2}}}}}{4} - \frac{1}{{2{z^3}}}\,dz}}\) Yechim
  6. \( \displaystyle \int_{{ - 2}}^{4}{{{x^6} - {x^4} + \frac{1}{{{x^2}}}\,dx}}\) Yechim
  7. \( \displaystyle \int_{{ - 4}}^{{ - 1}}{{{x^2}\left( {3 - 4x} \right)\,dx}}\) Yechim
  8. \( \displaystyle \int_{2}^{1}{{\frac{{2{y^3} - 6{y^2}}}{{{y^2}}}\,dy}}\) Yechim
  9. \( \displaystyle \int_{0}^{{\frac{\pi }{2}}}{{7\sin \left( t \right) - 2\cos \left( t \right)\,dt}}\) Yechim
  10. \( \displaystyle \int_{0}^{\pi }{{\sec \left( z \right)\tan \left( z \right) - 1\,dz}}\) Yechim
  11. \( \displaystyle \int_{{\frac{\pi }{6}}}^{{\frac{\pi }{3}}}{{2{{\sec }^2}\left( w \right) - 8\csc \left( w \right)\cot \left( w \right)\,dw}}\) Yechim
  12. \( \displaystyle \int_{0}^{2}{{{{\bf{e}}^x} + \frac{1}{{{x^2} + 1}}\,dx}}\) Yechim
  13. \( \displaystyle \int_{{ - 5}}^{{ - 2}}{{7{{\bf{e}}^y} + \frac{2}{y}\,dy}}\) Yechim
  14. \( \displaystyle \int_{0}^{4}{{f\left( t \right)\,dt}}\), bu erda \(f\left( t \right) = \left\{ {\begin{array}{*{20}{c}}{2t}&{t > 1}\\{1 - 3{t^2}}&{t \le 1}\end{array}} \right.\) Yechim
  15. \( \displaystyle \int_{{ - 6}}^{1}{{g\left( z \right)\,dz}}\), bu erda \(g\left( z \right) = \left\{ {\begin{array}{*{20}{c}}{2 - z}&{z > - 2}\\{4{{\bf{e}}^z}}&{z \le - 2}\end{array}} \right.\) Yechim
  16. \( \displaystyle \int_{3}^{6}{{\left| {2x - 10} \right|\,dx}}\) Yechim
  17. \( \displaystyle \int_{{ - 1}}^{0}{{\left| {4w + 3} \right|\,dw}}\) Yechim