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Find f. f '(t) = 2 cos t + sec?t, , -1/2 < t < «/2, _f(x/3) = 3 f(t) =

Find f. f '(t) = 2 cos t + sec?t, , -1/2 < t < «/2, _f(x/3) = 3 f(t) =

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Problem Statement:** Find \( f \). Given: \[ f'(t) = 2 \cos t + \sec^2 t, \quad -\pi/2 < t < \pi/2, \quad f(\pi/3) = 3 \] **Expression to Solve:** \[ f(t) = \] **Assistance Options:** "Need Help?" - **Read It** - **Watch It** **Explanation:** The problem provides the derivative \( f'(t) \) of a function \( f(t) \) and asks to find the original function \( f(t) \). The derivative is given as a sum of trigonometric functions. Additionally, a specific value of the function at \( t = \pi/3 \) is also given to help find the constant of integration. The expression must be integrated concerning \( t \) to find \( f(t) \).
Transcribed Image Text:**Problem Statement:** Find \( f \). Given: \[ f'(t) = 2 \cos t + \sec^2 t, \quad -\pi/2 < t < \pi/2, \quad f(\pi/3) = 3 \] **Expression to Solve:** \[ f(t) = \] **Assistance Options:** "Need Help?" - **Read It** - **Watch It** **Explanation:** The problem provides the derivative \( f'(t) \) of a function \( f(t) \) and asks to find the original function \( f(t) \). The derivative is given as a sum of trigonometric functions. Additionally, a specific value of the function at \( t = \pi/3 \) is also given to help find the constant of integration. The expression must be integrated concerning \( t \) to find \( f(t) \).
Expert Solution
Step 1: Given information

Given:

The derivative function f'(t)=2cost+sec2t , -π2<t<π2 , fπ3=3.

To find : 

The function f(t).

 Formula Used: 

The integration of the trigonometric functions is as follows,

∫cosx dx=sinx + C∫sec2x dx=tanx + C

where C is the integrating constant.

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