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Chapter 4: Q. 34 (page 404)

Fill in the blanks to complete each of the following integration formulas.
For $b > 0$ and $b$ not equal to 1 $鈭� b^{x} d x$ $= . . . . . . . . . . .$

Short Answer

Expert verified

The value is $鈭� b^{x} d x = \frac{1}{I n b} b^{x} + C$ .

Step by step solution

Step 1. Given information .

Consider the given integral $鈭� b^{x} d x$ for this $b > 0$ and $b$ not equal to 1 .

Step 2. Fill the blank for ∫bx dx .

The integral of the basic function $鈭� b^{x}$ $d x$ for $b > 0$ and $b$ not equal to 1 is ,

$鈭� b^{x} d x = \frac{1}{I n b} b^{x} + C$

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Most popular questions from this chapter

Explain why at this point we don鈥檛 have an integration formula for the function $f (x) = s e c x$ whereas we do have an integration formula for $f (x) = \sin x$ .

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

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

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

${鈭�}_{鈭� 3}^{2} 鈥� \frac{2 x}{x^{2} + 5} d x$

Calculate the exact value of each definite integral in Exercises 47鈥�52 by using properties of definite integrals and the formulas in Theorem 4.13.

${鈭�}_{0}^{4} ((2 x - 3)^{2} + 5) d x$

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

${鈭�}_{1}^{4} 鈥� \frac{2 x + 3}{x^{2} + 3 x + 4} d x$

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Fill in the blanks to complete each of the following integration formulas.For b>0and bnot equal to 1 鈭�bxdx=...........

Short Answer

Step by step solution

Step 1. Given information .

Step 2. Fill the blank for ∫bx dx .

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Fill in the blanks to complete each of the following integration formulas.
For $b > 0$ and $b$ not equal to 1 $鈭� b^{x} d x$ $= . . . . . . . . . . .$