Define f(x)=integral from 0 to x sin (t)dt, x >= 0.

Teresa Manning

Teresa Manning

Answered question

2023-02-04

Define fx= integral from 0toxsin(t)dt,x0. Then
A) F is increasing only in the interval 0,π2
B) f is decreasing in the interval 0,π
C) f attains maximum at x=π2
D) f attains minimum at x=π
E) f attains maximum at x=π

Answer & Explanation

udahnulizwk

udahnulizwk

Beginner2023-02-05Added 5 answers

The correct answer is A) f is increasing only in the interval 0,π2
Explanation for correct option:
Step-1: Integrate the function.
Given, f ( x ) = 0 x sin ( t ) d t
=-cost0x=-cosx-cos0
fx=1-cosx
Step-2: Differentiate the function.
f'x=0--sinx
f'x=sinx
We know that sinxis greater than zero.
Thus, fis increasing in interval 0,π2
Thus, correct answer is A.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?