/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 60 Suppose \(\int_{1}^{x} f(t) d t=... [FREE SOLUTION] | 91影视

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Chapter 5: Problem 60

Suppose \(\int_{1}^{x} f(t) d t=x^{2}-2 x+1 .\) Find \(f(x)\)

Short Answer

Expert verified
The function \(f(x)\) corresponding to the given integral is \(f(x)=2x-2\).

Step by step solution

01

Differentiate the given equation

The first step is to differentiate both sides of the equation \(\int_{1}^{x} f(t) dt=x^{2}-2x+1\). From the Fundamental Theorem of Calculus, the derivative of \( \int_{1}^{x} f(t) dt\) with respect to \(x\) is \(f(x)\). Thus, \(f(x)= \frac{d}{dx}(x^{2}-2x+1)\).
02

Apply the power rule

We now compute the derivative of \(x^{2}-2x+1\), which can be obtained easily by using the power rule: reduce the power by one and multiply by the original power. This gives us \(f(x)=2x-2\).
03

Finish

No further steps are required as this equation is our final solution.

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Most popular questions from this chapter

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