If ${I_1} = \int_0^1 {{2^{{x^2}}}dx,\;} {I_2} = \int_0^1 {{2^{{x^3}}}dx} ,\;{I_3} = \int_1^2 {{2^{{x^2}}}dx} $,${I_4} = \int_1^2 {{2^{{x^3}}}dx} $, then
${I_3} = {I_4}$
${I_3} > {I_4}$
${I_2} > {I_1}$
${I_1} > {I_2}$
For $x \in R$, let $f(x)=|\sin x|$ and $g(x)=\int_0^x f(t) d t .$ Let $p(x)=g(x)-\frac{2}{\pi} x$ Then
If $\int_{}^{} {f(x)\,dx} = x{e^{ - \log |x|}} + f(x),$ then $f(x)$ is
Let the function $f :[0,2] \rightarrow R$ be defined as
$f(x)=\left\{\begin{array}{cc}e^{\min \left[x^2, x-[x]\right\}}, & x \in[0,1) \\e^{\left[x-\log _e x\right]}, & x \in[1,2]\end{array}\right.$
where [t] denotes the greatest integer less than or equal to $t$. Then the value of the integral $\int \limits_0^2 x f(x) d x$ is
The minimum value of the function $f(x)=\int \limits_0^2 e^{|x-t|} d t$ is
If $\alpha \in (2 , 3) $ then number of solution of the equation $\int\limits_0^\alpha {} \cos (x + \alpha^2)\, dx = \sin \,\alpha$ is :