List of top Mathematics Questions on Definite Integral asked in CBSE CLASS XII

Find: \[ \int \frac{x^2}{(x^2-1)(x^2+4)}\,dx \]
If \(\int_{0}^{1} \frac{dx}{e^x + e^{-x}} = \tan^{-1}e + k\), then the constant value of \(k\) is:
The integral \( \int_{-1}^{1} (1 - |x|) \, dx \) is equal to :
Evaluate the definite integral: \[ \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} (\sin |x| + \cos |x|)_~dx \]
Use integration to find the area of the region enclosed by the curve $y = -x^2$ and the straight lines $x = -3$, $x = 2$ and $y = 0$. Sketch a rough figure to illustrate the bounded region.