Find the area under the given curve over the indicated interval
\[
y=2 x, \quad[3,5]
\]

The area under the curve is $\square$. (Simplify your answer.)

Answer

Expert–verified

Hide Steps

Answer

Final Answer: The area under the curve is $\boxed{16}$.

Steps

Step 1 ：The area under a curve y=f(x) from x=a to x=b is given by the definite integral ∫ from a to b f(x) dx.

Step 2 ：In this case, the function is $y=2x$ and the interval is [3,5].

Step 3 ：So, we need to calculate the definite integral of $2x$ from 3 to 5.

Step 4 ：The area under the curve $y=2x$ from $x=3$ to $x=5$ is 16.

Step 5 ：Final Answer: The area under the curve is $\boxed{16}$.