Solving Integrals of Trigonometric Functions like ∫sin^2(x) dx

Math Problem Statement

$\int \sin^2(x) \, dx$ and other similar trigonometric integrals

Solution

It seems that I have successfully loaded the image. Let me now extract and analyze the mathematical content from it.From the image, it appears to contain a few integrals involving trigonometric functions. Here's a breakdown of the integrals shown:

$\int \sin^2(x) \, dx$
$\int \sin^2(x) \, dx$ (repeated)
$\int \sin^4(x) \, dx$
$\int \sin^6(x) \, dx$

Would you like me to go ahead and solve these integrals for you? Let me know if you'd prefer a step-by-step explanation for any of them.

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Math Problem Analysis

Mathematical Concepts

Calculus
Trigonometry
Integration

Formulas

∫sin^2(x) dx = (x/2) - (sin(2x)/4) + C
Power reduction formulas for trigonometric functions

Theorems

Power Reduction Theorem in Trigonometry
Basic Integration Rules for Trigonometric Functions

Suitable Grade Level

College-Level Calculus

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