AktiraAktira JEE
Subscribe
MathsJEE Main 22 Jan 2026, Shift 2·Q22·Numerical·Tough

Definite Integration · Definite integral properties

Let [ ∙ ][\,\bullet\,] be the greatest integer function. If α=∫064(x1/3−[x1/3])dx\alpha = \displaystyle\int_0^{64}\left(x^{1/3} - \left[x^{1/3}\right]\right)dx, then 1π∫0απ(sin⁡2θsin⁡6θ+cos⁡6θ)dθ\frac{1}{\pi}\int_0^{\alpha\pi}\left(\frac{\sin^2\theta}{\sin^6\theta + \cos^6\theta}\right)d\theta is equal to .

Video solution coming soon

We're animating every PYQ step by step. Subscribe to get them first.

Subscribe

See the full 22 Jan 2026, Shift 2 paper

More on Definite integral properties