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If you are looking for some problems with solutions you can find some by clicking on the "Practice Problems" link above.
If you are looking for some problems with solutions you can find some by clicking on the "Practice Problems" link above.
Section 7.8 : Improper Integrals
Determine if each of the following integrals converge or diverge. If the integral converges determine its value.
- \( \displaystyle \int_{4}^{\infty }{{2 - 4x + 6{x^2}\,dx}}\)
- \( \displaystyle \int_{0}^{5}{{\frac{1}{{4w - 20}}\,dw}}\)
- \( \displaystyle \int_{{ - 1}}^{2}{{\frac{3}{{\sqrt[6]{{4 - 2z}}}}\,dz}}\)
- \( \displaystyle \int_{{ - \infty }}^{0}{{x\,{{\bf{e}}^{2 + 3x}}\,dx}}\)
- \( \displaystyle \int_{0}^{\infty }{{x\,{{\bf{e}}^{2 + 3x}}\,dx}}\)
- \( \displaystyle \int_{2}^{\infty }{{\frac{1}{{{x^2} + 1}}\,dx}}\)
- \( \displaystyle \int_{0}^{3}{{\frac{1}{{{z^2} - 4z}}\,dz}}\)
- \( \displaystyle \int_{{ - \infty }}^{1}{{\frac{x}{{{x^2} + 1}}\,dx}}\)
- \( \displaystyle \int_{{ - 1}}^{2}{{\frac{1}{{{y^2} - 2y - 3}}\,dy}}\)
- \( \displaystyle \int_{{ - \infty }}^{0}{{\cos \left( w \right)\,dw}}\)
- \( \displaystyle \int_{{10}}^{\infty }{{\frac{1}{{{{\left( {5 - 2z} \right)}^2}}}\,dz}}\)
- \( \displaystyle \int_{{ - \infty }}^{\infty }{{\frac{{{z^3}}}{{{z^4} + 1}}\,dz}}\)
- \( \displaystyle \int_{1}^{4}{{\frac{1}{{2y - 6}}\,dy}}\)
- \( \displaystyle \int_{1}^{5}{{\frac{1}{{\sqrt[3]{{w - 2}}}}\,dw}}\)
- \( \displaystyle \int_{{ - 2}}^{1}{{\frac{{{{\bf{e}}^{\frac{1}{x}}}}}{{{x^2}}}\,dx}}\)
- \( \displaystyle \int_{{ - \infty }}^{\infty }{{{x^2}{{\bf{e}}^{{x^{\,3}}}}\,dx}}\)
- \( \displaystyle \int_{{ - \infty }}^{\infty }{{\frac{y}{{{{\left( {{y^2} + 1} \right)}^3}}}\,dy}}\)
- \( \displaystyle \int_{0}^{3}{{\frac{{{w^3}}}{{\sqrt {9 - {w^2}} }}\,dw}}\)
- \( \displaystyle \int_{{ - 3}}^{1}{{\frac{1}{{{w^2} + 2w}}\,dw}}\)
- \( \displaystyle \int_{0}^{\infty }{{\frac{{{{\bf{e}}^{\frac{1}{x}}}}}{{{x^2}}}\,dx}}\)
- \( \displaystyle \int_{0}^{\infty }{{\frac{1}{{z{{\left[ {\ln \left( z \right)} \right]}^2}}}\,dz}}\)
- \( \displaystyle \int_{0}^{\infty }{{\frac{1}{{w - 1}}\,dw}}\)