Find a positive constant that satisfies the equation:∫(1/x²+a²)dx=1 integration limits: [ 0, +∞] Choose an option:a. a=π/4b. a=2/πc. a=2πd. a=π/2 Encontre uma constante positiva a que satisfaz a equacãodz =1Escolha uma opcão:O aa=O b.a =Oca= 2xO da=

Consider the equation ∫0∞1x2+a2dx=1 We have to find the value of a Use integral formula…

Answered: Find a positive constant that satisfies…

Find a positive constant that satisfies the equation: ∫(1/x²+a²)dx=1 integration limits: [ 0, +∞] Choose an option: a. a=π/4 b. a=2/π c. a=2π d. a=π/2

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter3: Additional Topics In Trigonometry

Section: Chapter Questions

Problem 22T

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Concept explainers

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus.

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.

Question

100%

Find a positive constant that satisfies the equation:

∫(1/x²+a²)dx=1 integration limits: [ 0, +∞]

Choose an option:

a. a=π/4

b. a=2/π

c. a=2π

d. a=π/2

Encontre uma constante positiva a que satisfaz a equacão
dz =1
Escolha uma opcão:
O aa=
O b.a =
Oca= 2x
O da=

With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.

Expert Solution

Step 1

Consider the equation $\int_{0}^{\infty} \frac{1}{x^{2} + a^{2}} d x = 1$

We have to find the value of $a$

Use integral formula $\int \frac{1}{x^{2} + a^{2}} d x = \frac{1}{a} \tan^{- 1} (\frac{x}{a}) + c$

Hence,

$\begin{matrix} \int_{0}^{\infty} \frac{1}{x^{2} + a^{2}} d x = 1 \\ {[\frac{1}{a} \tan^{- 1} (\frac{x}{a})]}_{0}^{\infty} = 1 \end{matrix}$

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