Evaluate the integral.
$\int_{- 5}^{- 4} (\frac{y^{6} - 7 y}{y^{5}}) d y$

Answer

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Answer

The value of the integral is $- \frac{108427}{24000}$ .

Steps

Step 1 ：Rewrite the integral by dividing each term in the numerator by $y^{5}$ . This results in two separate integrals: $\int_{- 5}^{- 4} y d y - 7 \int_{- 5}^{- 4} \frac{1}{y^{4}} d y$ .

Step 2 ：Solve the first integral using the power rule for integrals, which states that $\int x^{n} d x = \frac{1}{n + 1} x^{n + 1}$ . The result is $- \frac{9}{2}$ .

Step 3 ：Solve the second integral using the power rule for integrals, but first rewrite $\frac{1}{y^{4}}$ as $y^{- 4}$ . The result is $\frac{61}{24000}$ .

Step 4 ：Add the results of the two integrals to get the final result: $- \frac{9}{2} + \frac{61}{24000} = - \frac{108427}{24000}$ .

Step 5 ：The value of the integral is $- \frac{108427}{24000}$ .

Evaluate the integral.∫−5−4(y6−7yy5)dy

Answer

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Evaluate the integral.
$\int_{- 5}^{- 4} (\frac{y^{6} - 7 y}{y^{5}}) d y$