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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 6.1 : Average Function Value
For problems 1 – 4 determine \({f_{{\rm{avg}}}}\) for the function on the given interval.
- \(f\left( x \right) = 8{x^4} - 7{x^3} + 2\) on \(\left[ { - 2,1} \right]\)
- \(f\left( x \right) = \left( {4 - x} \right){{\bf{e}}^{{x^{\,2}} - 8x}}\) on \(\left[ {1,4} \right]\)
- \(f\left( x \right) = 6x - \frac{{4x}}{{{x^2} + 1}}\) on \(\left[ { - 3,0} \right]\)
- \(f\left( x \right) = \cos \left( {3x} \right){\left[ {2 + \sin \left( {3x} \right)} \right]^4}\) on \(\left[ {0,\frac{\pi }{6}} \right]\)
- \(f\left( x \right) = 10 - 4x - 6{x^2}\) on \(\left[ {2,6} \right]\)
- \(f\left( x \right) = 7{x^2} + 2x - 3\) on \(\left[ { - 1,1} \right]\)
- \(f\left( x \right) = 9 - 2{{\bf{e}}^{4x + 1}}\) on \(\left[ { - 1,2} \right]\)
- \(f\left( x \right) = 8 - \cos \left( {\frac{x}{4}} \right)\) on \(\left[ {0,4\pi } \right]\)