List of top Mathematics Questions on Definite and indefinite integrals asked in AP EAMCET

Evaluate the integral: \[ I = \int_{-5\pi}^{5\pi} \left(1 - \cos 2x \right)^{\frac{5}{2}} dx. \]
If \( A = \int_0^{\infty} \frac{1 + x^2}{1 + x^4} dx \) and \( B = \int_0^1 \frac{1 + x^2}{1 + x^4} dx \), then:
If \( \int_0^{2\pi} (\sin^4 x + \cos^4 x) \, dx = K \int_0^\pi \sin^2 x \, dx + L \int_0^\frac{\pi}{2} \cos^2 x \, dx \) and \( K, L \in \mathbb{N} \), then the number of possible ordered pairs \( (K, L) \) is}