7. $[-1 / 2$ Points $]$
DETAILS SCALC9 4.3.025.EP.
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PRACTICE ANOTHER
Find the general indefinite integral. (Use $C$ for the constant of integration.)
\[
\int\left(x^{2}+2 x-5\right) d x
\]
Evaluate the definite integral.
\[
\int_{7}^{9}\left(x^{2}+2 x-5\right) d x
\]
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Answer
And the definite integral of the function \(x^{2}+2 x-5\) from 7 to 9 is \(\boxed{\frac{452}{3}}\)
Step 1 ：Define the function as \(f = x^{2} + 2x - 5\)
Step 2 ：Calculate the indefinite integral of the function, which results in \(\frac{1}{3}x^{3} + x^{2} - 5x + C\)
Step 3 ：Calculate the definite integral of the function from 7 to 9, which results in \(\frac{452}{3}\)
Step 4 ：So, the general indefinite integral of the function \(x^{2}+2 x-5\) is \(\boxed{\frac{1}{3}x^{3} + x^{2} - 5x + C}\)
Step 5 ：And the definite integral of the function \(x^{2}+2 x-5\) from 7 to 9 is \(\boxed{\frac{452}{3}}\)
