List of top Mathematics Questions on Definite Integral asked in MHT CET

If \(I_n = \int _0^{π/4}tan^nx dx,n\in N\) then \(I_{n+2}+I_n\) is equal to

The value of the integral \(\int _{1/e}^e\frac{|logx|}{x^2}dx\) is

If \(\int _0^1\frac{dx}{\sqrt{x+1}-\sqrt{x}} = \sqrt{2}k\), then the value of \(k\) is...

If \([x]\) denotes the greatest integer less than or equal to \(x\), then the value of the integral \(\int _0^2x^2[x]\,dx\) is equal to

The value of integral \(\int _0^{\infty}\frac{1}{1+e^x}\,dx\) is...

If \(f(x) = |5x-3|\) is defined on interval \([0,1]\), then the value of \(\int _0^1f(x)\,dx\) is...

The value of \(\int _2^4(\{x\}+[x])\,dx =\)...(where \(\{x\}\) and \([x]\) are the fractional part function and the greatest integer function, respectively)

If \([x]\) is the greatest integer function not greater than \(x\), then the value of \(\int _0^2x[x^2]\,dx\) is...

\(\int _0^2|4x-5|\,dx = \ldots\)

The value of the definite integral \(\int _0^{log_e5}\frac{e^x\sqrt{e^x-1}}{e^x+3}\,dx\) is equal to...

If \([\cdot ]\) denotes the greatest integer function, then \(\int _0^{π/3}[tanx]\,dx =\)

The function \(f(x) = \int _0^x\frac{dt}{1+cost}\) satisfies which of the following differential equations?

If \(\int _a^b(x^2-x)\,dx = 18,\int _a^bx^3\,dx = 0\), then \(a+b\) is equal to

If \(I_n = \int _1^e(log_ex)^n\,dx\) where \(n\in Z^+\) and \(I_m+mI_{2026} = e\), then \(m =\)

The value of integral \(\int _0^1cot^{-1}(1+x^2-x)\,dx\) is...

\(\int _0^{log5}\frac{e^x\sqrt{e^x-1}}{e^x+3}\,dx =\)

\(\int _0^π|sin2x|\,\text{d}x =\)

\(\int _0^{log10}[\frac{e^x\sqrt{e^x-1}}{e^x+8}]dx =\)

If \(\int _0^a(x^2-4x+1)dx = 6\), then the real value of \(a\) is

If \(\int _0^a\frac{dx}{1+4x^2} = \frac{π}{8}\), then \(a =\)

If \(\int _2^e[\frac{1}{logx}-\frac{1}{(logx)^2}]dx = a+\frac{b}{log2}\), then values of \(a\) and \(b\) are

\(\int _0^3\sqrt{9-x^2}dx =\)

If \([\cdot ]\) denotes the greatest integer function, then \(\int _1^4x[x]dx\) is equal to

If \(\int _1^a(2x+1)dx = 5\), then the sum of the values of \(a\) is..

If \(n\) is an odd natural number and \[ I_n=\int_0^1 e^x(x-1)^n\,dx \] then \( I_n+nI_{n-1} \) is equal to: