নির্দিষ্ট যোগজ
∫01ex{x2+2x}dx \int_{0}^{1} e^{x} \left \lbrace x^{2} + 2 x \right \rbrace dx ∫01ex{x2+2x}dx কত?
e
-e
2e
-2e
∫01ex{x2+2x}dx=∫01ex{x2+ddx(x2)}dx=[x2ex]01=e \begin{array}{l}\int_{0}^{1} e^{x}\left\{x^{2}+2 x\right\} d x \\ =\int_{0}^{1} e^{x}\left\{x^{2}+\frac{d}{d x}\left(x^{2}\right)\right\} d x \\ =\left[x^{2} e^{x}\right]_{0}^{1}=e \quad \ { }\end{array} ∫01ex{x2+2x}dx=∫01ex{x2+dxd(x2)}dx=[x2ex]01=e
∫0π/2cosxdx= কত? \int_{0}^{\pi / 2} \cos x d x=\text { কত? } ∫0π/2cosxdx= কত?
f(x)= {x+1forx=0 \left \lbrace \begin{matrix} x + 1 & f{\quad\text{or}\quad} & x & = & 0 \end{matrix} \right . {x+1forx=0 হলে-
∫−1−12f(x)dx=18 \int_{- 1}^{- \frac{1}{2}} f{\left ( x \right )} dx = \frac{1}{8} ∫−1−21f(x)dx=81
∫01f(x)dx=0 \int_{0}^{1} f{\left ( x \right )} dx = 0 ∫01f(x)dx=0
f(−1)=1 f{\left ( - 1 \right )} = 1 f(−1)=1
নিচের কোনটি সঠিক?
∫1e2dxx(1+lnx) \int_{1}^{e^{2}} \frac{dx}{x \left ( 1 + \ln{x} \right )} ∫1e2x(1+lnx)dx এর মান কত?
α এর মান কত হলে ∫1α{2+xln(x2+5)}dx+∫1α{3−xln(x2+5)}dx \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 ∫1α{2+xln(x2+5)}dx+∫1α{3−xln(x2+5)}dx =30
