Question

Evaluate the integral $\int \sec^4 \theta \tan \theta d\theta$. (A) $\frac{1}{4} \sec^4 \theta + C$ (B) $\frac{1}{10} \tan^2 \theta \sec^5 \theta + C$ (C) $\frac{1}{5} \sec^5 \theta + C$ (D) $\frac{1}{2} \sec^2 \theta \tan^2 \theta + C$ (E) $\frac{1}{3} \sec^3 \theta + C$

Name: evaluate the integral int sec4 theta tan theta dtheta a frac14 sec4 theta c b frac110 tan2 theta sec5 theta c c frac15 sec5 theta c d frac12 sec2 theta tan2 theta c e frac13 sec3 theta c 58615
Uploaded: 2024-03-25T04:34:26-08:00
Duration: 3 min 27 s
Channel: Audrey Fong
Description: evaluate the integral int sec4 theta tan theta dtheta a frac14 sec4 theta c b frac110 tan2 theta sec5 theta c c frac15 sec5 theta c d frac12 sec2 theta tan2 theta c e frac13 sec3 theta c 58615

          Evaluate the integral $\int \sec^4 \theta \tan \theta d\theta$.
(A) $\frac{1}{4} \sec^4 \theta + C$
(B) $\frac{1}{10} \tan^2 \theta \sec^5 \theta + C$
(C) $\frac{1}{5} \sec^5 \theta + C$
(D) $\frac{1}{2} \sec^2 \theta \tan^2 \theta + C$
(E) $\frac{1}{3} \sec^3 \theta + C$

$evaluate the integral int sec4 theta tan theta dtheta a frac14 sec4 theta c b frac110 tan2 theta sec5 theta c c frac15 sec5 theta c d frac12 sec2 theta tan2 theta c e frac13 sec3 theta c 58615$

Added by Alex J.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Audrey Fong

03/25/2024

Step 1

We can rewrite the integrand as $\sec^3 \theta \cdot \sec \theta \tan \theta$. Let $u = \sec \theta$. Then, the differential $du$ is $du = \frac{d}{d\theta}(\sec \theta) d\theta = \sec \theta \tan \theta d\theta$. Now, substitute $u$ and $du$ into the Show more…

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Evaluate the integral $\int \sec^4 \theta \tan \theta d\theta$. (A) $\frac{1}{4} \sec^4 \theta + C$ (B) $\frac{1}{10} \tan^2 \theta \sec^5 \theta + C$ (C) $\frac{1}{5} \sec^5 \theta + C$ (D) $\frac{1}{2} \sec^2 \theta \tan^2 \theta + C$ (E) $\frac{1}{3} \sec^3 \theta + C$