Question

For each of the following integrals find an appropriate trigonometric substitution of the form x = f(t) to simplify the integral. a. ?(4x^2 - 2)^{3/2} dx x = sqrt(2/4)sec(t) b. ? x^2 / ?(3x^2 + 6) dx x = sqrt(6/3)tan(t) c. ? x ?(5x^2 - 40x + 76) dx x = d. ? x / ?(-13 - 5x^2 + 20x) dx x =

          For each of the following integrals find an appropriate trigonometric substitution of the form x = f(t) to simplify the integral.
a. ?(4x^2 - 2)^{3/2} dx
x = sqrt(2/4)sec(t)
b. ? x^2 / ?(3x^2 + 6) dx
x = sqrt(6/3)tan(t)
c. ? x ?(5x^2 - 40x + 76) dx
x =
d. ? x / ?(-13 - 5x^2 + 20x) dx
x =

For each of the following integrals find an appropriate trigonometric substitution of the form x = f(t) to simplify the integral.
a. ?(4x^2 - 2)^3/2 dx
x = sqrt(2/4)sec(t)
b. ? x^2 / ?(3x^2 + 6) dx
x = sqrt(6/3)tan(t)
c. ? x ?(5x^2 - 40x + 76) dx
x =
d. ? x / ?(-13 - 5x^2 + 20x) dx
x =

Added by Luc-A R.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert David Nguyen

01/27/2022

Step 1

This simplifies the integral to: $\int \sqrt{2}\sec(t)\sqrt{2\tan^2(t)}\sqrt{2}\sec(t)\tan(t) dt$ For the second integral, we have: $\int \frac{dx}{\sqrt{3x^2 + 6}}$ We can use the substitution $x = \sqrt{\frac{2}{3}}\tan(t)$, so $dx = Show more…

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For each of the following integrals find an appropriate trigonometric substitution of the form x = f(t) to simplify the integral. a. ∫(4x^2 - 2)^{3/2} dx x = sqrt(2/4)sec(t) b. ∫ x^2 / √(3x^2 + 6) dx x = sqrt(6/3)tan(t) c. ∫ x √(5x^2 - 40x + 76) dx x = d. ∫ x / √(-13 - 5x^2 + 20x) dx x =