List of top Mathematics Questions

Evaluate the integral: \[ \int \frac{\cos \theta}{2 - \sin^2 \theta} \, d\theta \]

Integrating factor of \[ \frac{dy}{dx} - 2y = 2x - 3 \]

If \[ (a - 2)^2 + (b - 2)^2 + (c - 2)^2 = 0, \text{ then } a + b + c = \]

If \[ (a - 2)^2 + (b - 2)^2 + (c - 2)^2 = 0, \text{ then } a + b + c = \]

Evaluate the integral: \[ \int \frac{\log(1+x)}{1+x} \, dx \]

Evaluate the limit: \[ \lim_{x \to 2} \frac{(x^3 - 8) \sin(x - 2)}{x^2 - 4x + 4} \]

Length of latus rectum of ellipse \[ \frac{x^2}{9} + \frac{y^2}{16} = 1 \]

Evaluate the integral: \[ \int_{-3}^{3} \left\lfloor x \right\rfloor \, dx \]

Find the center of the ellipse given by the equation \[ 4x^2 + 24x + 9y^2 - 18y + 9 = 0 \]

Find the minimum of the function \[ f(x) = |x+2| \]

Evaluate the following integral: \[ \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \left( x^4 + x^3 + x \right) \cos x \, dx \]

Given the following probabilities: \[ P(A) = 0.7, P(B) = 0.5, P(A \cup B) = 0.9, \quad \text{find} \quad P(A/B) \]

If $ a_n = 2^{n-1} $, where $ n = 1, 2, 3, ... $, then find $ \sum_{n=1}^{20} a_n $.

Solve for $ \alpha $ if: $ \cos^{-1}(2 \sin \alpha) = \frac{47}{12} $

Evaluate the integral: $ \int e^{-x} \cdot e^{3x} \, dx $

Given that $ x = \frac{\sin^2 \theta}{\tan \theta - \sec \theta}, \quad y = \frac{\sec \theta + \tan \theta}{\sec^2 \theta}, \quad \text{find} \, \frac{y}{x} $

Evaluate the integral: $ \int \frac{1}{x(x^4 + 1)} \, dx $