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Found in: Page 306

### Essential Calculus: Early Transcendentals

Book edition 2nd
Author(s) James Stewart
Pages 830 pages
ISBN 9781133112280

# Evaluate the indefinite integral$$\int {{{\sec }^2}2} \theta d\theta$$.

The indefinite integral value of the given equation is$$\int {{{\sec }^2}} 2\theta d\theta = \frac{1}{2}\tan \theta + c$$.

See the step by step solution

## Step 1 Definition of the indefinite integral

An integral that has no upper bound and no lower bound is known as indefinite integral.

## Step 2: Expand the number of variables in the equation.

Given: $$I = \int {{{\sec }^2}} 2\theta d\theta$$

Known value $$\int {{{\sec }^2}} axdx = \frac{1}{a}\tan ax + c$$

## Step 3: Evaluate the equation.

Put$$a = 2,x = \theta$$

So, $$I = \frac{1}{2}\tan 2\theta + c$$

Therefore, the indefinite integral value of the given equation is$$\int {{{\sec }^2}} 2\theta d\theta = \frac{1}{2}\tan \theta + c$$.