List of top Mathematics Questions on Integral Calculus asked in MET

If \( \int f(x)\,dx = g(x) \), then \( \int x^9 f(x^5)\,dx \) is equal to

If \[ \int \sin^2 t \tan^{-1}\sqrt{\frac{1-x}{1+x}}\,dx = A\sin^{-1}x + B\sqrt{1-x^2} + C, \] then \(A+B\) is equal to

By Simpson’s \(1/3\)rd rule, the approximate value of the integral \(\int_1^2 e^{-x/2}dx\) using four intervals, is

If \(I_n = \int \sin^n x dx\), then \(nI_n - (n - 1)I_{n-2}\) equals

If \(\int f(x) dx = F(x)\), then \(\int x^3 f(x^2) dx\) is equal to

The approximate value of \(\int_1^5 x^2 dx\) using trapezoidal rule with \(n = 4\) is

If \( f(x) = \int_0^1 e^{|t - x|} \, dt \) for \( 0 \leq x \leq 1 \), then the maximum value of \( f(x) \) is:

In a triangle, the length of the two larger sides are 24 and 22, respectively. If the angles are in AP, then the third side is

\(G\) is a set of all rational numbers except \(-1\) and \(*\) is defined by \(a*b = a + b + ab\) for all \(a,b \in G\). In the group \((G,*)\) the solution of \(2^{-1} * x * 3^{-1} = 5\) is

The value of \(\int_a^b \frac{|x|}{x} dx\) is

If \( \frac{2x + 3}{(x + 1)(x - 3)} = \frac{a}{x + 1} + \frac{b}{x - 3} \), then \( a + b \) is equal to

If \( \frac{2x + 3}{(x + 1)(x - 3)} = \frac{a}{x + 1} + \frac{b}{x - 3} \), then \( a + b \) is equal to

If \( \frac{e^x + 2}{(e^x - 1)(2e^x - 3)} = -\frac{3}{e^x - 1} + \frac{B}{2e^x - 3} \), then \( B \) is equal to