Answer:
the area of the curve y= f(x) = x between x = 5 and x = 10
[tex]A=\frac{75}{2}[/tex]
Step-by-step explanation:
Using the Area formula
[tex]A=\int _a^b\:f\left(x\right)dx[/tex]
As the area of curve lies between x = 5 and x = 10
so
so the integral expression becomes
[tex]A=\int _5^{10}xdx[/tex]
[tex]\mathrm{Apply\:the\:Power\:Rule}:\quad \int x^adx=\frac{x^{a+1}}{a+1},\:\quad \:a\ne -1[/tex]
[tex]A=\left[\frac{x^{1+1}}{1+1}\right]^{10}_5[/tex]
[tex]=\left[\frac{x^2}{2}\right]^{10}_5[/tex]
[tex]=\frac{1}{2}\left[10^2-5^2\right][/tex]
[tex]=\frac{1}{2}\cdot \:75[/tex]
[tex]=\frac{75}{2}[/tex]
Therefore, area of the curve y= f(x) = x between x = 5 and x = 10
[tex]A=\frac{75}{2}[/tex]
