Question

Use the trigonometric substitution $x = \frac{7}{9}sin(t)$ to put the integral in terms of $t$: $\int \frac{1}{\sqrt{49 - 81x^2}}dx = \int$ $dt$ Antideriving results in the following expression in terms of $t$: $+C$ Putting this answer in terms of $x$ results in the following answer: $+C$

          Use the trigonometric substitution $x = \frac{7}{9}sin(t)$ to put the integral in terms of $t$:
$\int \frac{1}{\sqrt{49 - 81x^2}}dx = \int$  $dt$
Antideriving results in the following expression in terms of $t$:
$+C$
Putting this answer in terms of $x$ results in the following answer:
$+C$

Use the trigonometric substitution x = (7)/(9)sin(t) to put the integral in terms of t:
∫(1)/(√(49 - 81x^2))dx = ∫ dt
Antideriving results in the following expression in terms of t:
+C
Putting this answer in terms of x results in the following answer:
+C

Added by Andr-S N.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

08/18/2023

Step 1

This gives us ∫(1/√(49-81((7/9)(-sin(t)))^2)) * (7/9)(-cos(t)) dt = ∫(1/√(49-49sin^2(t))) * (7/9)(-cos(t)) dt Show more…

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Use the trigonometric substitution x = (7/9)sin(t) to put the integral in terms of t: ∫(1/√(49-81x^2))dx = ∫dt Antideriving results in the following expression in terms of t: +C Putting this answer in terms of x results in the following answer: +C Use the trigonometric substitution x = (7/9)(-sin(t)) to put the integral in terms of t: ∫dt √(49-81x^2) Antideriving results in the following expression in terms of t: +C Putting this answer in terms of x results in the following answer: +C