Question

Find the area of the curve y= f(x) = x between x = 5 and x = 10

Answer 1

Answer:

the area of the curve y= f(x) = x between x = 5 and x = 10

$A=\frac{75}{2}$

Step-by-step explanation:

• Finding the area of the curve  y = f(x) = x between x = 5 and x = 10

Using the Area formula

$A=\int _a^b\:f\left(x\right)dx$

As the area of curve lies between x = 5 and x = 10

so

• a = 5, b = 10

so the integral expression becomes

$A=\int _5^{10}xdx$

$\mathrm{Apply\:the\:Power\:Rule}:\quad \int x^adx=\frac{x^{a+1}}{a+1},\:\quad \:a\ne -1$

$A=\left[\frac{x^{1+1}}{1+1}\right]^{10}_5$

    $=\left[\frac{x^2}{2}\right]^{10}_5$

     $=\frac{1}{2}\left[10^2-5^2\right]$

     $=\frac{1}{2}\cdot \:75$

     $=\frac{75}{2}$

Therefore, area of the curve y= f(x) = x between x = 5 and x = 10

$A=\frac{75}{2}$