Chapter 5: Q. 44 (page 478)

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

Short Answer

Expert verified

The value is $\infty (D i v e r g e n t) .$

Step by step solution

Step 1. Given Information.

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

Step 2. Value of the integral.

On solving,

$= \lim_{b \to {\frac{π}{2}}^{-}} (\int_{0}^{b} \tan x d x) = \lim_{b \to {\frac{π}{2}}^{-}} (\ln | \sec x |]_{0}^{b} = \lim_{b \to {\frac{π}{2}}^{-}} (\ln | \sec b | - \ln | \sec 0 |) = \ln (\infty) - 0 = \infty = D i v e r g e n t .$

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

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/2tanxdx

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.
$\int_{0}^{π / 2} \tan x d x$