List of top Mathematics Questions on Integral Calculus asked in IIT JAM EN

The area under the curve \[ f(x)=x^5e^{x^3} \] between \(x=1\) and \(x=2\) is
The value of the derivative of the function \( y = x e^x \) at \( x = 1 \) is ........... (rounded off to two decimal places).

The value of the integral \[ \int_{0}^{9} \frac{x - 1}{1 + \sqrt{x}} \, dx \] is _____________. (in integer) 
 

Let $f$ be a function defined on $\left(-\dfrac{\pi}{2}, \dfrac{\pi}{2}\right)$ as \[ f(x) = \frac{\cos\left(\dfrac{\pi}{2} + |x|\right)}{\sin\left(\dfrac{\pi}{2} - |x|\right)}. \] Then,