Question

Use a definite integral to find the area under the curve between the given x-values. f(x) = 3 x from x = 1 to x = 8

Answer 1

Answer: 94.5

Step-by-step explanation:

Given

Function is $f(x)=3x$ and the boundary is $x=1\ \text{to}\ x=8$

Integrating the function

$\Rightarrow I=\int_{1}^{8}f(x)dx\\\\\Rightarrow I=\int_{1}^{8}3xdx\\\\\Rightarrow I=\left ( \frac{3x^2}{2} \right )_1^8\\\Rightarrow I=1.5(8^2-1^2)=1.5(64-1)\\\Rightarrow I=94.5$

The value of integral is 94.5