List of top Mathematics Questions on Definite Integral asked in NEST

The limit \[ \lim_{n \to \infty} \frac{1}{\sqrt{n}} \left[ 1 + \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{3}} + \dots + \frac{1}{\sqrt{n}} \right] \]

The definite integral \[ \int_{\pi/2}^{\pi} \frac{\sin x - x \cos x}{x(x + \sin x)} \, dx \] equals

Evaluate \[ \int_{0}^{\sqrt{\pi}} x\sin^{2}(x^{2})\,dx \]