Answer:
-2.92178
Step-by-step explanation:
Given the function [tex]f(x)=3x\ sin x[/tex]
The average,A is calculated using the formula;
[tex]A=\frac{1}{b-a}\int\limits^a_b F(x)\, dx \\\\A=\frac{1}{7-1}\int\limits^7_1 3x \ Sin \ x\, dx \\\\\\=\frac{3}{6}\int\limits^7_1 x \ Sin \ x\, dx \\\\\#Integration\ by\ parts, u=x, v \prime=sin(x)\\=0.5[-xcos(x)-\int-cos(x)dx]\limits^7_1\\\\=0.5[-xcos(x)-(-sin(x))]\limits^7_1\\\\=0.5[-xcos(x)+sin(x)]\limits^7_1\\\\=0.5[-6.82595--0.98240]\\\\=-2.92178[/tex]
Hence, the average of the function is -2.92178
Integration is way of uniting the part to find a whole.The average value of the given function is -2.922.
The given function is,
[tex]f(x)=3xsinx[/tex]
Average value of function can be given as,
[tex]A=\dfrac{1}{b-a}\times\int\limits^b_a {f(x}) \, dx }[/tex]
Put the values,
[tex]A=\dfrac{1}{7-1}\times\int\limits^7_1 {3xsinx) \, dx }[/tex]
[tex]A=\dfrac{3}{6}\times\int\limits^7_1 {xsiinx \, dx }[/tex]
Integration is way of uniting the part to find a whole.
Use integration by parts method to solve the above integration,
[tex]A=\dfrac{3}{2}\times [-xcos+xsiinx ]^{7} _{1}[/tex]
[tex]A=\dfrac{3}{2}\times [-6.826+0.982][/tex]
[tex]A=-2.922[/tex]
Thus, the average value of the given function is -2.922.
For more about the integration, follow the link below
https://brainly.com/question/18651211
