List of top Mathematics Questions on Integral Calculus asked in LPUNEST

\(\tan^{-1}(1) - \sec^{-1}2)\) is equal to:(
If the radius of a circle increases at a uniform rate of \(2\ \text{cm/s}\), then the rate of increase of area of the circle, at the approximate instant when the radius is \(20\ \text{cm}\), is:
If \(\cos x = \tan y,\ \cot y = \tan z\) and \(\cot z = \tan x\), then \(\sin x\) is equal to:
The integral \[ \int\!\frac{\sin^2x\cos^2x}{(\sin^5x+\cos^3x\sin^2x+\sin^3x\cos^2x+x^5+x\cos^5x)}dx \] is of the form}
If \[ \int \sin(101x)\,\sin^{99}x\,dx = \frac{\sin(100x)\sin^{100}x}{k+5}+c, \] then \(\dfrac{k}{19}=\)
If \(g(x)=\cos x^2\), \(f(x)=\sqrt{x}\) and \(\alpha,\beta\;(\alpha<\beta)\) are the roots of \(18x^2-9\pi x+\pi^2=0\), then the area bounded by the curve \(y=(g\circ f)(x)\) and the lines \(x=\alpha,\;x=\beta\) and \(y=0\) is:
The ratio in which $\hat{i}+2\hat{j}+3\hat{k}$ divides the join of $-2\hat{i}+3\hat{j}+5\hat{k}$ and $7\hat{i}-\hat{k}$ is
Consider the following statements \[ P:\ \text{Suman is brilliant} \] \[ Q:\ \text{Suman is rich} \] \[ R:\ \text{Suman is honest} \] The negation of the statement “Suman is brilliant and dishonest if and only if Suman is rich” can be expressed as:
10 men and 6 women are to be seated in a row so that no two women sit together. The number of ways they can be seated is