$\int_{0}^{\frac{\pi}{6}} \sin ^{2} x \cos x d x=$ কত ?

 f(x)=  $\left \lbrace \begin{matrix} x + 1 & f{\quad\text{or}\quad} & x & = & 0 \end{matrix} \right .$  হলে-

1.   $\int_{- 1}^{- \frac{1}{2}} f{\left ( x \right )} dx = \frac{1}{8}$

2.   $\int_{0}^{1} f{\left ( x \right )} dx = 0$

3.   $f{\left ( - 1 \right )} = 1$

নিচের কোনটি সঠিক?

$\int_{1}^{e^{2}} \frac{dx}{x \left ( 1 + \ln{x} \right )}$ এর মান কত?

α এর মান কত হলে $\int_{1}^{\alpha} \left \lbrace 2 + x \ln{\left ( x^{2} + 5 \right )} \right \rbrace dx + \int_{1}^{\alpha} \left \lbrace 3 - x \ln{\left ( x^{2} + 5 \right )} \right \rbrace dx$   =30 

$\int_{0}^{1} \frac{e^{x}}{e^{x}+1} d x$ এর মান কত?