Question

Evaluate the following integral. \[ \int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} 3 \sqrt{\sec ^{2} \theta-1} d \theta \] \[ \int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} 3 \sqrt{\sec ^{2} \theta-1} d \theta= \] \( \qquad \) (Type an exact answer.)

          Evaluate the following integral.
\[
\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} 3 \sqrt{\sec ^{2} \theta-1} d \theta
\]
\[
\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} 3 \sqrt{\sec ^{2} \theta-1} d \theta=
\]
\( \qquad \)
(Type an exact answer.)

Evaluate the following integral.

∫-(π)/(4)^(π)/(4) 3 √(sec ^2θ-1) d θ

∫-(π)/(4)^(π)/(4) 3 √(sec ^2θ-1) d θ=

(Type an exact answer.)

Added by Amber G.

Calculus Volume 2

Gilbert Strang, 1st Edition

Chapter 3

Instant Answer

Solved by Expert Scott Stetson

Step 1

Therefore, the integral can be rewritten as: \[ \int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} 3 \sqrt{\sec^2 \theta - 1} \, d\theta = \int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} 3 \sqrt{\tan^2 \theta} \, d\theta \] Show more…

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Evaluate the following integral. \[ \int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} 3 \sqrt{\sec ^{2} \theta-1} d \theta \] \[ \int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} 3 \sqrt{\sec ^{2} \theta-1} d \theta= \] \( \qquad \) (Type an exact answer.)