Question

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

Answer 1

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

`A=(75)/(2)`

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=(x^(a+1))/(a+1),\:\quad \:a\\e -1`

`A=\left[(x^(1+1))/(1+1)\right]^(10)_5`

`=\left[(x^2)/(2)\right]^(10)_5`

`=(1)/(2)\left[10^2-5^2\right]`

`=(1)/(2)\cdot \:75`

`=(75)/(2)`

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

`A=(75)/(2)`