Chapter 5: Problem 44
Multiple Choice \(\int_{-4}^{4}(4-|x|) d x=\) \((\mathbf{A}) 0 \quad\) (B) 4\(\quad\) (C) 8 (D) 16\(\quad\) (E) 32
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In Exercises 13-18, (a) use Simpson's Rule with n = 4 to approximate the value of the integral and (b) find the exact value of the integral to check your answer. (Note that these are the same integrals as Exercises 1-6, so you can also compare it with the Trapezoidal Rule approximation.) $$\int_{1}^{2} \frac{1}{x} d x$$
In Exercises \(15-18,\) find the average value of the function on the interval without integrating, by appealing to the geometry of the region between the graph and the \(x\) -axis. $$f ( t ) = \sin t , \quad [ 0,2 \pi ]$$
In Exercises \(23-26\) use a calculator program to find the Simpson's Rule approximations with \(n=50\) and \(n=100 .\) $$\int_{0}^{\pi / 2} \frac{\sin x}{x} d x$$
In Exercises \(19-30,\) evaluate the integral using antiderivatives, as in Example \(4 .\) $$\int _ { 3 } ^ { 7 } 8 d x$$
In Exercises \(27-40\) , evaluate each integral using Part 2 of the Fundamental Theorem. Support your answer with NINT if you are unsure. $$\int_{0}^{\pi}(1+\cos x) d x$$
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