Mathematics, 21.07.2019 21:50 leximae2186
Find the average value of f over region d. f(x, y) = 4x sin(y), d is enclosed by the curves y = 0, y = x2, and x = 7.
Answers: 1
![\frac{1}{ \frac{343}{3} } \int\limits^7_0 \int\limits^{x^2}_0 {4x\sin(y)} \, dydx = -\frac{3}{343} \int\limits^7_0 {4x\cos(x^2)} \, dx \\ \\ =-\frac{3}{343} \int\limits^{49}_0 {2\cos(t)} \, dt=-\frac{6}{343} \left[\sin(t)\right]_0^{49} \, dt=-\frac{6}{343}\sin49](/tpl/images/0117/0907/316b8.png)
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Find the average value of f over region d. f(x, y) = 4x sin(y), d is enclosed by the curves y = 0, y...
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