Given the right triangle pictured in Fig. 5-6: (a) Find the average value of h. (b)...

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Given the right triangle pictured in Fig. 5-6: (a) Find the average value of h. (b) At what point does this average value occur? (c) Determine average value of the f(x) = sin ¹x, 0 ≤ x ≤ 1/1/0 (Use integration by parts.) (d) Determine the average value of f(x) = cos²x, 0 ≤ x ≤ π 2° H -x. According to the mean value theorem for integrals, B the average value of the function h on the interval [0, B] is (a) h(x) = == A B 2 = B 1 B 0 H -x dx B - Η HE 2 X B Fig. 5-6 H X (b) The point, §, at which the average value of h occurs may be obtained by equating f(§) with that average value, i.e., H H § = B 2 Thus, & Given the right triangle pictured in Fig. 5-6: (a) Find the average value of h. (b) At what point does this average value occur? (c) Determine average value of the f(x) = sin ¹x, 0 ≤ x ≤ 1/1/0 (Use integration by parts.) (d) Determine the average value of f(x) = cos²x, 0 ≤ x ≤ π 2° H -x. According to the mean value theorem for integrals, B the average value of the function h on the interval [0, B] is (a) h(x) = == A B 2 = B 1 B 0 H -x dx B - Η HE 2 X B Fig. 5-6 H X (b) The point, §, at which the average value of h occurs may be obtained by equating f(§) with that average value, i.e., H H § = B 2 Thus, &