Problem 48
Multiple Choice If \(\int _ { 2 } ^ { 5 } f ( x ) d x = 12\) and \(\int _ { 5 } ^ { 8 } f ( x ) d x = 4\) then all of the following must be true except (A) $$\int _ { 2 } ^ { 8 } f ( x ) d x = 16$$ (B) $$\int _ { 2 } ^ { 5 } f ( x ) d x - \int _ { 5 } ^ { 8 } 3 f ( x ) d x = 0$$ (C) $$\int _ { 5 } ^ { 2 } f ( x ) d x = - 12$$ (D) $$\int _ { - 5 } ^ { - 8 } f ( x ) d x = - 4$$ (E) $$\int _ { 2 } ^ { 6 } f ( x ) d x + \int _ { 6 } ^ { 8 } f ( x ) d x = 16$$
Problem 49
In Exercises \(47-56,\) use graphs, your knowledge of area, and the fact that \(\quad\) $$\int_{0}^{1} x^{3} d x=\frac{1}{4}$$ to evaluate the integral. $$\int_{2}^{3}(x-2)^{3} d x$$
Problem 49
In Exercises \(49-54,\) use NINT to solve the problem. Evaluate \(\int_{0}^{10} \frac{1}{3+2 \sin x} d x\)
Problem 49
Multiple Choice What is the average value of the cosine function on the interval [ 1,5 ] ? \(\begin{array} { l l } { \text { (A) } - 0.990 } & { ( \text { B) } - 0.450 } \\\ { \text { (D) } 0.412 } & { ( \text { E) } 0.998 } \end{array}\)
Problem 50
In Exercises \(47-56,\) use graphs, your knowledge of area, and the fact that \(\quad\) $$\int_{0}^{1} x^{3} d x=\frac{1}{4}$$ to evaluate the integral. $$\int_{-1}^{1}|x|^{3} d x$$
Problem 50
Multiple Choice If the average value of the function \(f\) on the interval \([ a , b ]\) is \(10 ,\) then \(\int _ { a } ^ { b } f ( x ) d x =\) (A) \(\frac { 10 } { b - a } \quad\) (B) \(\frac { f ( a ) + f ( b ) } { 10 } \quad\) (C) \(10 b - 10 a\) \(( \mathbf { D } ) \frac { b - a } { 10 } \quad ( \mathbf { E } ) \frac { f ( b ) + f ( a ) } { 20 }\)
Problem 50
In Exercises \(49-54,\) use NINT to solve the problem. Evaluate \(\int_{-0.8}^{0.8} \frac{2 x^{4}-1}{x^{4}-1} d x\)
Problem 51
In Exercises \(47-56,\) use graphs, your knowledge of area, and the fact that \(\quad\) $$\int_{0}^{1} x^{3} d x=\frac{1}{4}$$ to evaluate the integral. $$\int_{0}^{1}\left(1-x^{3}\right) d x$$
Problem 52
In Exercises \(47-56,\) use graphs, your knowledge of area, and the fact that \(\quad\) $$\int_{0}^{1} x^{3} d x=\frac{1}{4}$$ to evaluate the integral. $$\int_{-1}^{2}(|x|-1)^{3} d x$$
Problem 52
In Exercises \(49-54,\) use NINT to solve the problem. Find the average value of \(\sqrt{\cos x}\) on the interval \([-1,1]\)
