JEE Advanced Definite Integrals — practice questions
30 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice JEE Advanced Definite Integrals in the app →$\displaystyle\int_0^\pi in x\, dx = ?$If $f$ is **odd** on $[-a, a]$, then $\displaystyle\int_{-a}^{a} f(x)\, dx$ equals:$\displaystyle\int_0^1 \dfrac{1}{1 + x^2}\, dx = ?$$\displaystyle\int_0^{\pi/2} in^2 x\, dx = ?$$\displaystyle\int_0^\pi x in x\, dx = ?$$\displaystyle\int_1^e \ln x\, dx = ?$If $\displaystyle I_n = \int_0^{\pi/2} in^n x\, dx$, then $I_5 = ?$$\displaystyle\int_0^2 [x]\, dx$ where $[x]$ is the greatest integer function:Evaluate $\displaystyle\int_0^{10\pi} | in x|\, dx$:$\dfrac{d}{dx}\left[\displaystyle\int_0^{x^2} in(t^2)\, dt\right] = ?$$\displaystyle\int_0^{\pi/2} \dfrac{ in x}{ in x + \cos x}\, dx = ?$$\displaystyle\int_0^{\pi/2} \log( in x)\, dx = ?$ (classic)$\displaystyle\int_0^{\pi/2} \log(\tan x)\, dx = ?$$\displaystyle\int_0^\pi \dfrac{x in x}{1 + \cos^2 x}\, dx = ?$$\displaystyle\int_0^1 \dfrac{\ln(1+x)}{1+x^2}\, dx = ?$ (Putnam classic)Evaluate $\displaystyle\lim_{n\to\infty} um_{r=1}^{n} \dfrac{1}{n + r}$$\displaystyle\int_0^1 x^2(1-x)^3\, dx = ?$ (Beta function)$\displaystyle\int_{-\pi/2}^{\pi/2} \dfrac{ in^2 x}{1 + e^x}\, dx = ?$ (Glasser-type)$\displaystyle\int_0^\infty x^3 e^{-x}\, dx = ?$$\displaystyle\int_1^e (\ln x)^2\, dx = ?$If $f(x)$ is continuous and $\displaystyle\int_0^x f(t)\, dt = x^2(1 + x)$, then $f(2) = ?$$\displaystyle\int_0^1 \dfrac{x^4(1-x)^4}{1 + x^2}\, dx = ?$ (Putnam — pinpoints $22/7 - \pi$)$\displaystyle\int_0^{\pi/4} \tan^4 x\, dx = ?$$\displaystyle\int_0^\pi \dfrac{x}{1 + in x}\, dx = ?$Evaluate $\displaystyle\lim_{n\to\infty} \dfrac{1^k + 2^k + \cdots + n^k}{n^{k+1}}$ for $k > -1$:$\displaystyle\int_0^{\pi/2} \dfrac{dx}{1 + \tan^3 x} = ?$If $\displaystyle f(x) = \int_0^x t in t\, dt$, then $f''(\pi) = ?$Given $\displaystyle\int_0^{\pi/2} \dfrac{ in^n x}{ in^n x + \cos^n x}\, dx$, the value is:$\displaystyle\int_0^1 \dfrac{x - 1}{\ln x}\, dx = ?$ (Frullani-type)$\displaystyle\int_0^{\infty} \dfrac{\ln x}{1 + x^2}\, dx = ?$