Calculus I - Computing Definite Integrals (Assignment Problems)

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Section 5.7 : Computing Definite Integrals

Evaluate each of the following integrals.
1. $\displaystyle \int{{3{z^2} - 4 + \frac{4}{{{z^2}}}\,dz}}$
2. $\displaystyle \int_{1}^{4}{{3{z^2} - 4 + \frac{4}{{{z^2}}}\,dz}}$
3. $\displaystyle \int_{{ - 2}}^{1}{{3{z^2} - 4 + \frac{4}{{{z^2}}}\,dz}}$
1. $\displaystyle \int{{6x + \frac{1}{{3x}}\,dx}}$
2. $\displaystyle \int_{0}^{7}{{6x + \frac{1}{{3x}}\,dx}}$
3. $\displaystyle \int_{3}^{7}{{6x + \frac{1}{{3x}}\,dx}}$
Evaluate each of the following integrals.
1. $\displaystyle \int{{\sin \left( y \right) + {{\sec }^2}\left( y \right)\,dy}}$
2. $\displaystyle \int_{0}^{{\frac{\pi }{4}}}{{\sin \left( y \right) + {{\sec }^2}\left( y \right)\,dy}}$
3. $\displaystyle \int_{0}^{{\frac{{2\pi }}{3}}}{{\sin \left( y \right) + {{\sec }^2}\left( y \right)\,dy}}$

Evaluate each of the following integrals, if possible. If it is not possible clearly explain why it is not possible to evaluate the integral.

$\displaystyle \int_{0}^{3}{{10t - 6{t^2} + 9\,dt}}$
$\displaystyle \int_{{ - 1}}^{4}{{24{z^2} + 5{z^4}dz}}$
$\displaystyle \int_{1}^{0}{{9w - 3{w^2} + 4{w^3}\,dw}}$
$\displaystyle \int_{{ - 3}}^{{ - 1}}{{15{t^2} - 10t - 2dt}}$
$\displaystyle \int_{{ - 2}}^{4}{{{v^3} - 7{v^2} + 3v\,dv}}$
$\displaystyle \int_{0}^{{16}}{{9\sqrt x + 10\,\sqrt[4]{x}\,dx}}$
$\displaystyle \int_{{ - 1}}^{2}{{8\,\,\sqrt[3]{z} - 12\,\,\sqrt[5]{z}\,dz}}$
$\displaystyle \int_{1}^{4}{{\sqrt {{y^5}} - \frac{1}{{\sqrt[3]{y}}}\,dy}}$
$\displaystyle \int_{1}^{4}{{\frac{6}{{{x^3}}} - \frac{1}{{3{x^2}}}\,dx}}$
$\displaystyle \int_{6}^{{ - 3}}{{8{w^3} - 25{w^4} + \frac{4}{{3{w^5}}}\,dw}}$
$\displaystyle \int_{{ - 1}}^{{ - 3}}{{\frac{4}{{3{z^2}}} - \frac{6}{{{z^3}}}\,dz}}$
$\displaystyle \int_{0}^{6}{{\left( {3 - t} \right)\left( {2{t^2} + 3} \right)\,dt}}$
$\displaystyle \int_{4}^{1}{{\sqrt x \left( {x - 2{x^2} + 1} \right)\,dx}}$
$\displaystyle \int_{2}^{5}{{\frac{{6{z^5} - 8{z^4} + 2{z^2}}}{{{z^4}}}\,dz}}$
$\displaystyle \int_{{ - 2}}^{{ - 4}}{{\frac{{9{x^4} - 8{x^3} + x}}{{3{x^2}}}\,dx}}$
$\displaystyle \int_{{ - 8}}^{2}{{\frac{{7{v^{10}} + 4{v^6} - 3{v^2}}}{{{v^5}}}\,dv}}$
$\displaystyle \int_{1}^{2}{{\frac{{\left( {y - 2} \right)\left( {y + 2} \right)}}{{{y^2}}}\,dy}}$
$\displaystyle \int_{0}^{{\frac{\pi }{4}}}{{8{{\sec }^2}\left( t \right) + 2\sec \left( t \right)\tan \left( t \right)\,dt}}$
$\displaystyle \int_{{ - \,\frac{\pi }{3}}}^{{\frac{\pi }{6}}}{{3\cos \left( w \right) + \sin \left( w \right)\,dw}}$
$\displaystyle \int_{{ - \,\frac{\pi }{4}}}^{{\frac{\pi }{4}}}{{12{{\sec }^2}\left( y \right) - 9{{\csc }^2}\left( y \right)\,dy}}$
$\displaystyle \int_{{\frac{{2\pi }}{3}}}^{{\frac{\pi }{4}}}{{3\sin \left( v \right) + 8\csc \left( v \right)\cot \left( v \right)\,dv}}$
$\displaystyle \int_{{ - 3}}^{1}{{4x - 7{{\bf{e}}^x}\,dx}}$
$\displaystyle \int_{{ - 2}}^{1}{{\frac{{4{{\bf{e}}^{2w}} + 4w\,{{\bf{e}}^w}}}{{{{\bf{e}}^w}}}\,dw}}$
$\displaystyle \int_{0}^{{\frac{1}{2}}}{{\frac{3}{{\sqrt {1 - {x^2}} }} + \frac{7}{{{x^2} + 1}}\,dx}}$
$\displaystyle \int_{{ - 2}}^{3}{{5\sin \left( t \right) + \frac{1}{{\sqrt {1 - {t^2}} }}\,dt}}$
$\displaystyle \int_{6}^{{10}}{{\frac{4}{z} + \frac{1}{{2{z^2}}}\,dz}}$
$\displaystyle \int_{1}^{6}{{2{x^3} + \frac{3}{{8x}}\,dx}}$
$\displaystyle \int_{{ - 4}}^{{ - 1}}{{f\left( t \right)\,dt}}$ where $f\left( t \right) = \left\{ {\begin{array}{*{20}{c}}{9 + 6{t^2}}&{t > - 3}\\{8t}&{t \le - 3}\end{array}} \right.$
$\displaystyle \int_{{ - 2}}^{4}{{g\left( x \right)\,dx}}$ where $g\left( x \right) = \left\{ {\begin{array}{*{20}{c}}{9 - 2{{\bf{e}}^x}}&{x > 0}\\{8\sin \left( x \right)}&{x \le 0}\end{array}} \right.$
$\displaystyle \int_{4}^{9}{{h\left( w \right)\,dw}}$ where $h\left( w \right) = \left\{ {\begin{array}{*{20}{c}}4&{w > 6}\\{3w + 1}&{w \le 6}\end{array}} \right.$
$\displaystyle \int_{{ - 1}}^{7}{{f\left( x \right)\,dx}}$ where $f\left( x \right) = \left\{ {\begin{array}{*{20}{c}}{9{x^2}} & {x > 5}\\{ - 7} & {1 < x \le 5}\\{3 - 8x} & {x \le 1}\end{array}} \right.$
$\displaystyle \int_{{ - 3}}^{1}{{\left| {8 + 4x} \right|\,dx}}$
$\displaystyle \int_{2}^{8}{{\left| {3v - 12} \right|\,dv}}$
$\displaystyle \int_{0}^{6}{{\left| {10 - 2z} \right|\,dz}}$
$\displaystyle \int_{{ - 3}}^{6}{{\left| {{t^2} - 4} \right|\,dt}}$