Chapter 5: Q. 43 (page 478)

Use limits of definite integrals to calculate each of the improper integrals in Exercises 21–56.
$\int_{0}^{π / 2} \sec x d x$

Short Answer

Expert verified

The answer is $\infty (D i v e r g e s) .$

Step by step solution

Step 1. Given information.

The given integral is $\int_{0}^{π / 2} \sec x d x$ .

Step 2. Value of the integral.

We know,

$\int s e c x = s e c x \tan x$

On simplifying,

$\int_{0}^{\frac{π}{2}} \sec (x) d x = [\ln | \sec x + \tan x |]_{0}^{\frac{π}{2}} = [\ln |\sec (\frac{π}{2}) + \tan (\frac{π}{2})| - \ln |\sec (\frac{π}{2}) + \tan (\frac{π}{2})|] = \infty (D i v e r g e s)$

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Use limits of definite integrals to calculate each of the improper integrals in Exercises 21–56.
$\int_{0}^{π / 2} \sec x d x$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Value of the integral.

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Use limits of definite integrals to calculate each of the improper integrals in Exercises 21–56.∫0π/2secxdx

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Value of the integral.

One App. One Place for Learning.

Most popular questions from this chapter

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Use limits of definite integrals to calculate each of the improper integrals in Exercises 21–56.
$\int_{0}^{π / 2} \sec x d x$