Math  /  Calculus

QuestionLet g(y)=7sin(y)g(y)=7 \sin (y) Determine the average value, g(c)g(c), of gg over [0,3π4]\left[0, \frac{3 \pi}{4}\right]. g(c)=g(c)= \square Determine the value(s) of cc in [0,3π4]\left[0, \frac{3 \pi}{4}\right] guaranteed by the Mean Value Theorem. Round the solution(s) to four decimal places, if necessary. c=c= \square

Studdy Solution
Calculate the approximate value of c c using the inverse sine function: c=arcsin(43π(22+1))c = \arcsin\left(\frac{4}{3\pi} \left(\frac{\sqrt{2}}{2} + 1\right)\right)
Compute c c to four decimal places.
The average value g(c) g(c) is approximately 43π(722+7) \boxed{\frac{4}{3\pi} \left(\frac{7\sqrt{2}}{2} + 7\right)} .
The value of c c is approximately arcsin(43π(22+1)) \boxed{\arcsin\left(\frac{4}{3\pi} \left(\frac{\sqrt{2}}{2} + 1\right)\right)} .

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