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Calculate the definite integral of sin²(x) from 0 to π. Find the solution to this trigonometric integral problem, demonstrating the use of the identity sin²(x) = (1-cos(2x))/2. The answer is π/2.

Calculate the double integral ∫₀²∫₀¹ x²y dx dy. Step-by-step solution reveals the answer is 2/3.

Find the derivative of the function h(x) = ln(x² + 1) using the chain rule. The derivative is h'(x) = 2x / (x² + 1).

Learn how to find the derivative of the function g(x) = sin(x) * e^x using the product rule of differentiation. The solution reveals that the derivative is g'(x) = e^x (sin(x) + cos(x)).

Learn how to find the derivative of the function f(x) = x² + 3x - 2 using the power rule, constant multiple rule, and sum/difference rule. The derivative is f'(x) = 2x + 3.

Simplify the algebraic expression (a + b)² - (a - b)² using the difference of squares pattern. The solution reveals a simplified expression of 4ab.

Find the sum of the first 1000 natural numbers. This math problem can be solved using the formula for arithmetic series, resulting in a sum of 500,500.

This SEO description explains how to find the derivative of the sum of sine and cosine functions. The problem asks for the derivative of sin(x) + cos(x), and the solution demonstrates the application of the sum rule and basic trigonometric derivatives to arrive at the answer: cos(x) - sin(x).

Learn how to find the limit of the rational function (3x² + 2x) / (x² + 1) as x approaches infinity. The solution reveals a simple technique for evaluating limits at infinity and arrives at the answer: 3.

Find the derivative of the polynomial function f(x) = x³ + 2x² - 5x + 3 using the power rule. The derivative is f'(x) = 3x² + 4x - 5.

Learn how to solve the definite integral ∫₀² (x² + 2x) dx, step-by-step, and discover the answer: 20/3.

Find the derivative of the polynomial function f(x) = x³ + 2x² - 5x + 3 using the power rule. The derivative is f'(x) = 3x² + 4x - 5.

Solve the absolute value inequality |x - 3| ≤ 4. The solution is -1 ≤ x ≤ 7.

Solve for x in the inequality 2x - 7 > 5. The solution is x > 6.

Solve the system of equations 2x + y = 8 and x - y = 1. The solution is x = 3 and y = 2.

Solve the quadratic equation x² + 5x + 6 = 0. Factoring the equation, we find the solutions are x = -2 and x = -3.

Solve the equation 3x - 7 = 20. Find the value of x in this simple algebraic equation. The solution is x = 9.

Find the height of a triangle with an area of 24 square centimeters and a base of 8 centimeters. The solution reveals the height to be 6 centimeters.

This math problem asks you to calculate the area of a composite shape made up of a rectangle and a triangle. The rectangle has a length of 7 cm and a width of 5 cm, while the triangle has a base of 4 cm and a height of 5 cm. The solution involves calculating the area of each shape individually and then adding them together to find the total area, which is 45 cm².

Find the sum of the first 100 positive odd numbers. The solution is 10,000.

Find the missing angle 'x' in a triangle where one angle is 80 degrees and the exterior angle adjacent to the 80-degree angle is 120 degrees. The solution is x = 140 degrees.

Solve for W in the equation W² + 5 = 30, then calculate W³ + 5. The possible solutions are 130 and -120.

Solve for P in the equation 2P(3 + P⁰) = 8. The solution is P = 1.

Solve the math problem: 25^x = 125. Find the value of x^2. The answer is 9/4 or 2.25.

Find the value of x in the equation (2x + 30) + (2x + 10) = 180. The solution is x = 35.

This math problem shows how to solve the equation X³ - X⁰ = 26 step-by-step. The solution is X = 3.

This math problem presents a sequence of numbers: 6, 12, 21, ?, 48. The goal is to identify the pattern and determine the missing number. By analyzing the differences between consecutive numbers, we discover a pattern of increasing by 3. Applying this pattern, we find the missing number to be 33.

This math problem asks which fraction is larger, 3/4 or 5/6. The solution explains how to find the least common denominator and convert the fractions to have the same denominator. The answer is that 5/6 is larger than 3/4.

This math problem asks to solve for x in the equation √(x+5) = 8. The solution is x = 59.

This math problem asks whether multiplying 4/5 by 8 will result in a number greater than or less than 8. The solution explains that multiplying by a fraction less than 1 results in a smaller number, and calculates the product to be 6.4, confirming that it is less than 8.