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Magazine Problem 21
In Exercises 21 through 30 , evaluate the indicated definite integral. \(\int_{0}^{1}\left(5 x^{4}-8 x^{3}+1\right) d x\)
Problem 22
In Exercises 21 through 30 , evaluate the indicated definite integral. \(\int_{1}^{4}\left(\sqrt{t}+t^{-3 / 2}\right) d t\)
Problem 24
In Exercises 21 through 30 , evaluate the indicated definite integral. \(\int_{1}^{9} \frac{x^{2}+\sqrt{x}-5}{x} d x\)
Problem 25
In Exercises 21 through 30 , evaluate the indicated definite integral. \(\int_{-1}^{2} 30(5 x-2)^{2} d x\)
Problem 29
In Exercises 21 through 30 , evaluate the indicated definite integral. \(\int_{0}^{e-1}\left(\frac{x}{x+1}\right) d x\)
Problem 30
In Exercises 21 through 30 , evaluate the indicated definite integral. \(\int_{e}^{e^{2}} \frac{1}{x(\ln x)^{2}} d x\)
Problem 32
AREA BETWEEN CURVES In Exercises 31 through 38 , sketch the indicated region \(R\) and find its area by integration. \(R\) is the region under the curve \(y=e^{x}+e^{-x}\) over the interval \(-1 \leq x \leq 1\).
Problem 34
AREA BETWEEN CURVES In Exercises 31 through 38 , sketch the indicated region \(R\) and find its area by integration. \(R\) is the region under the curve \(y=\sqrt{9-5 x^{2}}\) over the interval \(0 \leq x \leq 1\).
Problem 35
AREA BETWEEN CURVES In Exercises 31 through 38 , sketch the indicated region \(R\) and find its area by integration. \(R\) is the region bounded by the curve \(y=\frac{4}{x}\) and the line \(x+y=5\).
Problem 36
AREA BETWEEN CURVES In Exercises 31 through 38 , sketch the indicated region \(R\) and find its area by integration. \(R\) is the region bounded by the curves \(y=\frac{8}{x}\) and \(y=\sqrt{x}\) and the line \(x=8 .\)
