Question

Use the substitution formula, $\int_a^b f(g(x)) \cdot g'(x) dx = \int_{g(a)}^{g(b)} f(u) du$ where $g(x) = u$, to evaluate the following integral. $\int_0^{\frac{3\pi}{2}} \sqrt{8} \cos^2 \left( \frac{3}{6} \theta \right) d\theta$ $\int_0^{\frac{3\pi}{2}} \sqrt{8} \cos^2 \left( \frac{3}{6} \theta \right) d\theta = \square$ (Type an exact answer in terms of x.)

Name: use the substitution formula intab fgx cdot gx dx intgagb fu du where gx u to evaluate the following integral int0frac3pi2 sqrt8 cos2 left frac36 theta right dtheta int0frac3pi2 sqrt8 co 34002
Uploaded: 2022-02-23T10:39:15-08:00
Duration: 2 min 22 s
Channel: Maitreya T
Description: use the substitution formula intab fgx cdot gx dx intgagb fu du where gx u to evaluate the following integral int0frac3pi2 sqrt8 cos2 left frac36 theta right dtheta int0frac3pi2 sqrt8 co 34002

          Use the substitution formula, $\int_a^b f(g(x)) \cdot g'(x) dx = \int_{g(a)}^{g(b)} f(u) du$ where $g(x) = u$, to evaluate the following integral.
$\int_0^{\frac{3\pi}{2}} \sqrt{8} \cos^2 \left( \frac{3}{6} \theta \right) d\theta$
$\int_0^{\frac{3\pi}{2}} \sqrt{8} \cos^2 \left( \frac{3}{6} \theta \right) d\theta = \square$
(Type an exact answer in terms of x.)

$use the substitution formula intab fgx cdot gx dx intgagb fu du where gx u to evaluate the following integral int0frac3pi2 sqrt8 cos2 left frac36 theta right dtheta int0frac3pi2 sqrt8 co 34002$

Added by Kristen S.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Maitreya T

02/23/2022

Step 1

Then $du = \frac{1}{2} d\theta$, so $d\theta = 2du$. When $\theta = 0$, $u = 0$. When $\theta = \frac{3\pi}{2}$, $u = \frac{3\pi}{4}$. Then the integral becomes $\int_0^{\frac{3\pi}{4}} \sqrt{8} \cos^2 u \cdot 2 du = 2\sqrt{8} \int_0^{\frac{3\pi}{4}} \cos^2 u du$ Show more…

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Use the substitution formula, $\int_a^b f(g(x)) \cdot g'(x) dx = \int_{g(a)}^{g(b)} f(u) du$ where $g(x) = u$, to evaluate the following integral. $\int_0^{\frac{3\pi}{2}} \sqrt{8} \cos^2 \left( \frac{3}{6} \theta \right) d\theta$ $\int_0^{\frac{3\pi}{2}} \sqrt{8} \cos^2 \left( \frac{3}{6} \theta \right) d\theta = \square$ (Type an exact answer in terms of x.)