Evaluate.
\[
\int_{2}^{3}\left(5 x^{2}+6\right) d x
\]
$\int_{2}^{3}\left(5 x^{2}+6\right) d x=\square$ (Type an integer or a simplified fraction.)

Answer

Expert–verified

Hide Steps

Answer

The definite integral of the function $5x^2 + 6$ from $2$ to $3$ is $\boxed{\frac{113}{3}}$.

Steps

Step 1 ：The function to be integrated is $5x^2 + 6$.

Step 2 ：The antiderivative of $5x^2$ is $\frac{5}{3}x^3$ and the antiderivative of $6$ is $6x$.

Step 3 ：So, the antiderivative of the function is $\frac{5}{3}x^3 + 6x$.

Step 4 ：We need to evaluate this antiderivative at $x = 3$ and $x = 2$ and subtract the two results to find the definite integral.

Step 5 ：The definite integral of the function $5x^2 + 6$ from $2$ to $3$ is $\boxed{\frac{113}{3}}$.