Math Problem Statement

câu 3

Cho F(1) = 1, F(a) = 4. Tìm F(x) và g(x), với g(x) = ∫_1^x f(t) dt.

Solution

The third problem in the image reads:

  1. Given:
    F(1)=1,F(a)=4F(1) = 1, F(a) = 4
    Find F(x)F(x) and g(x)g(x), where g(x)=∫1xf(t)dtg(x) = \int_1^x f(t) dt.

To solve this, we need to find f(x)f(x) from the provided conditions and then determine the function g(x)g(x).

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Math Problem Analysis

Mathematical Concepts

Integration
Definite Integrals
Fundamental Theorem of Calculus

Formulas

g(x) = ∫_1^x f(t) dt

Theorems

Fundamental Theorem of Calculus

Suitable Grade Level

Grades 11-12

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