Math Problem Statement

Evaluate the definite integrals given in the image: 1) ∫ from -2 to 3 (x² - 7x) dx 2) ∫ from 1 to 4 (5 - x³) dx 3) ∫ from 1 to 3 (3x³ + x² - 6) dx

Solution

The image you uploaded contains a list of definite integrals. Here are the integrals provided in the image:

  1. ∫−23(x2−7x) dx\int_{-2}^{3} (x^2 - 7x) \, dx
  2. ∫14(5−x3) dx\int_{1}^{4} (5 - x^3) \, dx
  3. ∫13(3x3+x2−6) dx\int_{1}^{3} (3x^3 + x^2 - 6) \, dx

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Math Problem Analysis

Mathematical Concepts

Definite Integrals
Integral Calculus
Fundamental Theorem of Calculus

Formulas

∫ x^n dx = (x^(n+1)) / (n+1) + C
Fundamental Theorem of Calculus: ∫ from a to b f(x) dx = F(b) - F(a), where F(x) is the antiderivative of f(x)

Theorems

Fundamental Theorem of Calculus

Suitable Grade Level

Undergraduate or Advanced High School (Grades 11-12)

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