Calculate the Area Under the Curve y = x^2

Math Problem Statement

Вычислить площадь фигур, изображенных на рисунке

Solution

To calculate the area under the curve represented in the image, we need to compute the definite integral of the function $y = x^2 - 4x + 5$ from $x = 1$ to $x = 3$ .

The integral to compute is:

$A = \int_1^3 (x^2 - 4x + 5) \, dx$

Let me go ahead and calculate this integral for you.

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Math Problem Analysis

Mathematical Concepts

Calculus
Definite Integral
Quadratic Functions

Formulas

Integral of a quadratic function
Definite integral formula

Theorems

Fundamental Theorem of Calculus

Suitable Grade Level

Grades 11-12

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