Integration

The value of x such that x > 1, satisfying the equation $\int_{1}^{x} t \ln t \, dt = \frac{1}{4}$ is

Consider a probability distribution given by the density function P(x). P(x) = {Cx^2, for 1 ≤ x ≤ 4 0, for x 4 The probability that x lies between 2 and 3, i.e., P(2 ≤ x ≤ 3) is __...

Consider a probability distribution given by the density function $P(x)$. $$P(x)=\left\{\begin{array}{cc} C x^2, & \text { for } 1 \leq x \leq 4 \\ 0, & \text { for } x 4 \end{arra...

The value of $x$ such that $x>1$, satisfying the equation $\int_1^x t \ln t d t=\frac{1}{4}$ is

If $f(x) = R \sin (\frac{\pi x}{2}) + S$, $f' (\frac{1}{2}) = \sqrt{2}$ and $\int_0^1 f(x)dx = \frac{2R}{\pi}$, then the constants R and S are, respectively

If $$f\left( x \right)\,\,\, = \,\,\,R\,\sin \left( {{{\pi x} \over 2}} \right) + S.f'\left( {{1 \over 2}} \right) = \sqrt 2 $$ and $$\int_0^1 {f\left( x \right)dx = {{2R} \over \p...

A probability density function on the interval $$\left[ {a,1} \right]$$ is given by $$1/{x^2}$$ and outside this interval the value of the function is zero. The value of $$a$$ is _...

Let $$f(x)$$ be the continuous probability density function of a random variable X. The probability that $$a\, < \,X\, \le \,b$$, is: