Question

7) Let $b>1$ be a real number. Evaluate the integral $A(b) = \int_1^b \frac{dx}{\sqrt{24+x^2}}$ b) Use your answer from a) to determine the improper integral $\int_1^\infty \frac{dx}{\sqrt{24+x^2}}$ converges or diverges

          7) Let $b>1$ be a real number. Evaluate the integral
$A(b) = \int_1^b \frac{dx}{\sqrt{24+x^2}}$

b) Use your answer from a) to determine the improper integral $\int_1^\infty \frac{dx}{\sqrt{24+x^2}}$ converges or diverges

7) Let b>1 be a real number. Evaluate the integral
A(b) = ∫1^b (dx)/(√(24+x^2))

b) Use your answer from a) to determine the improper integral ∫1^∞(dx)/(√(24+x^2)) converges or diverges

Added by Patricia A.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Naresh Bagrecha

05/17/2021

Step 1

Then $dx = \sqrt{24} \sec^2 \theta d\theta$. When $x = 1$, $\tan \theta = \frac{1}{\sqrt{24}}$, so $\theta = \arctan(\frac{1}{\sqrt{24}})$. When $x = b$, $\tan \theta = \frac{b}{\sqrt{24}}$, so $\theta = \arctan(\frac{b}{\sqrt{24}})$. Then \begin{align*} Show more…

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7) Let $b > 1$ be a real number. Evaluate the integral $A(b) = \int_1^b \frac{dx}{\sqrt{24+x^2}}$ b) Use your answer from a) to determine the improper integral $\int_1^\infty \frac{dx}{\sqrt{24+x^2}}$ converges or diverges