List of top Mathematics Questions on Some Properties of Definite Integrals asked in CBSE CLASS XII

Evaluate : \( \int_{-\pi/2}^{\pi/2} \frac{\cos^2 x}{2^x + 1} \, dx \)
Evaluate the definite integral: \[ \int_{\frac{\pi}{12}}^{\frac{5\pi}{12}} \frac{1}{1 + \sqrt{\cot x}} \, dx \]
Evaluate: \[ \int_1^3 (|x - 1| + |x - 2| + |x - 3|) \, dx. \]
\( \int_{0}^{\pi/2} \frac{\sin x - \cos x}{1 + \sin x \cos x} \, dx \) is equal to:
Evaluate: \[ \int_{-2}^{2} \frac{x^3 + |x| + 1}{x^2 + 4|x| + 4} \, dx. \]
Evaluate: \[ \int_0^{\frac{\pi^2}{4}} \frac{\sin\sqrt{x}}{\sqrt{x}} \, dx \]
If \( f(x) \) is an odd function, then: \[ \int_{-\pi/2}^{\pi/2} f(x) \cos^3 x \, dx \, \text{equals:} \]