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Chapter 4: Q. 29 (page 362)

Use integration formulas to solve each integral in Exercises 21鈥�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.
$鈭� (3.2 {(1.43)}^{x} - 50) d x$

Short Answer

Expert verified

The solution of the integral is $3.2 (\frac{1 . 43^{x}}{\ln (1.43)}) - 50 x + C .$

Step by step solution

01

Step 1. Given Information.

The given integral is $鈭� (3.2 {(1.43)}^{x} - 50) d x .$

02

Step 2. Solve.

By solving the integral we get,

$鈭� (3.2 {(1.43)}^{x} - 50) d x = 3.2 鈭� {(1.43)}^{x} d x - 鈭� 50 d x Use 鈭� a^{x} = \frac{a^{x}}{\ln (a)} = 3.2 (\frac{1 . 43^{x}}{\ln (1.43)}) - 50 x + C$

03

Step 3. Verification.

To verify the answer we differentiate $3.2 (\frac{1 . 43^{x}}{\ln (1.43)}) - 50 x + C$ it.

On differentiating we get,

$3.2 (\frac{1 . 43^{x}}{\ln (1.43)}) - 50 x + C = \frac{3.2}{\ln (1.43)} {(1.43)}^{x} - 50 x + C = 8.94 {(1.43)}^{x} - 50 x + C = \frac{d}{d x} 8.94 {(1.43)}^{x} - \frac{d}{d x} (50 x) + \frac{d}{d x} (C) = 3.2 {(1.43)}^{x} - 50$

Hence proved.

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Most popular questions from this chapter

Determine which of the limit of sums in Exercises 47鈥�52 are infinite and which are finite. For each limit of sums that is finite, compute its value.

$\lim_{n 鈫� 鈭�} {鈭�}_{k = 1}^{n} \frac{k^{2} + k + 1}{n}$

Verify that $鈭� \cot x d x = \ln (\sin x) + C$ . (Do not try to solve the integral from scratch.)

Use integration formulas to solve each integral in Exercises 21鈥�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. (Hint for Exercise 54: $\tan (x) = \frac{\sin (x)}{\cos (x)}$ ).

$鈭� \frac{2 x \ln x - x}{{(\ln x)}^{2}} d x .$

Use the Fundamental Theorem of Calculus to find the exact values of the given definite integrals. Use a graph to check your answer.

${鈭�}_{2}^{4} 鈥� 3 e^{2 x 鈭� 4} d x$

Use integration formulas to solve each integral in Exercises 21鈥�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.

$鈭� (x^{2} + 2^{x} + 2^{2}) d x$

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