📢 Shares

Find the integral of x² + 3x - 2. Solution: (x³)/3 + (3x²)/2 - 2x + C

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.