List of top Mathematics Questions on Definite Integrals asked in Bihar Board XII

Find the value of \[ \int_0^{\pi/2} x \cos x \, dx. \]

Evaluate: \[ \int_0^{\pi/2} \log (\cos x) \, dx. \]

Find the value of \[ \int_0^{\pi/2} \frac{dx}{1 + \sqrt{\tan x}}. \]

Find the value of \[ \int_0^a \sqrt{a^2 - x^2} \, dx. \]

Evaluate: \(\displaystyle \int_0^{\frac{\pi}{6}} \cos x \cdot \cos 2x \, dx = \)

Evaluate: \(\displaystyle \int_{-\pi}^{\pi} \tan x \, dx = \)

Evaluate: \(\displaystyle \int_0^4 \sqrt{x} \, dx = \)

Evaluate: \(\displaystyle \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \sin^7 x \, dx = \)

Evaluate: \(\displaystyle \int_0^a \left( \sqrt{x} + \sqrt{a - x} \right) \sqrt{x} \, dx = \)

Evaluate: \(\displaystyle \int_0^{\frac{\pi}{2}} \cos 2x \, dx = \)