List of top Mathematics Questions on Integrals of Some Particular Functions asked in JKCET

Here, $ [x] $ denotes the greatest integer less than or equal to $ x $ . Given that $ f(x) = [x] + x $ . The value obtained when this function is integrated with respect to $ x $ with lower limit as $ \frac{3}{2} $ and upper limit as $ \frac{9}{2} $ , is

The value of integral \(\int{e^x}(\frac{cosx+sinx}{cos^2x})dx\)

Integrate $ \frac{{{\sec }^{2}}\,({{\sin }^{-1}}x)}{\sqrt{1-{{x}^{2}}}} $

If $ f(x)={{\log }_{e}}\,(1+x)-{{\log }_{e}}(1-x), $ then the value of $ \int_{-1/2}^{1/2}{f(x)\,\,\,dx} $ equals to

If $ f(x)=\int_{1}^{x}{\sqrt{4-{{t}^{2}}}}\,\,\,dt, $ then real roots of the equation $ x-f'(x)=0 $ are

$ \int_{0}^{\pi /2}{\frac{{{\sin }^{100}}x}{{{\sin }^{100}}x+{{\cos }^{100}}x}\,\,dx} $ is equal to

$ \int{{{x}^{2}}\,{{7}^{x}}\,\,dx} $ is equal to

$ \int_{0}^{x}{\log \,(\cot \,x\,+\,\tan t)\,dt} $ =

If $ f\,(x)=\underset{y\to x}{\mathop{lim}}\,\,\frac{{{\sin }^{2}}y-{{\sin }^{2}}x}{{{y}^{2}}-{{x}^{2}}}, $ then $ \int{4x\,\,f(x)\,\,dx} $ =

$ 3a{{\int_{0}^{1}{\left( \frac{ax-1}{a-1} \right)}}^{2}}\,\,dx $ is equal to

$ \int{\frac{1}{1+\cos \,\,ax}}\,\,dx $ is equal to