Find the area under the given curve over the indicated interval.
\[
y=x^{2} ;[2,3]
\]
The area under the curve is (Simplify your answer.)
Answer
Final Answer: The area under the curve over the indicated interval is \(\boxed{\frac{19}{3}}\).
Step 1 ：The area under a curve from a to b is given by the definite integral from a to b of the function. In this case, the function is \(y = x^2\) and the interval is [2,3]. So, we need to calculate the definite integral of \(x^2\) from 2 to 3.
Step 2 ：The definite integral of \(x^2\) from 2 to 3 is calculated as \(\int_{2}^{3} x^2 dx\).
Step 3 ：After calculating the definite integral, we find that the area under the curve is \(\frac{19}{3}\).
Step 4 ：Final Answer: The area under the curve over the indicated interval is \(\boxed{\frac{19}{3}}\).
