Book edition 1st

Author(s) Peter Kohn, Laura Taalman

Pages 1155 pages

ISBN 9781429241861

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Short Answer

Use integration formulas to solve each integral in Exercises 21–62. You may have to use algebra, educated guess and-check, and/or recognize an integrand as the result of a product, quotient, or chain rule calculation. Check each of your answers by differentiating. $\int (x^{2} - 3 x^{5} - 7) d x$

The answer is $\frac{1}{3} x^{3} - (\frac{1}{2}) x^{6} - 7 x + C .$

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information.

The given integral is $\int (x^{2} - 3 x^{5} - 7) d x .$

Step 2. Integration.

On integrating,

$\int (x^{2} - 3 x^{5} - 7) d x = \int x^{2} d x - \int 3 x^{5} d x - \int 7 d x = \frac{1}{3} x^{3} - 3 (\frac{1}{6}) x^{6} - 7 x + C = \frac{1}{3} x^{3} - (\frac{1}{2}) x^{6} - 7 x + C$

Step 3. Verification.

On Differentiating $\frac{1}{3} x^{3} - (\frac{1}{2}) x^{6} - 7 x + C$ , we get,

$\frac{1}{3} \times 3 x^{2} - \frac{1}{2} \times 6 x^{5} - 7 = x^{2} - 3 x^{5} - 7$

Hence proved.

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Calculus

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Short Answer

Use integration formulas to solve each integral in Exercises 21–62. You may have to use algebra, educated guess and-check, and/or recognize an integrand as the result of a product, quotient, or chain rule calculation. Check each of your answers by differentiating. $\int (x^{2} - 3 x^{5} - 7) d x$

Step by Step Solution

Step 1. Given information.

Step 2. Integration.

Step 3. Verification.

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Use integration formulas to solve each integral in Exercises 21–62. You may have to use algebra, educated guess and-check, and/or recognize an integrand as the result of a product, quotient, or chain rule calculation. Check each of your answers by differentiating. ∫x2-3x5-7dx

Step by Step Solution

Step 1. Given information.

Step 2. Integration.

Step 3. Verification.

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Pure Maths

Use integration formulas to solve each integral in Exercises 21–62. You may have to use algebra, educated guess and-check, and/or recognize an integrand as the result of a product, quotient, or chain rule calculation. Check each of your answers by differentiating. $\int (x^{2} - 3 x^{5} - 7) d x$