নির্দিষ্ট যোগজ
∫01dx2x−x2=? \int_{0}^{1} \frac{dx}{\sqrt{2 x - x^{2}}} = ? ∫012x−x2dx=?
[RU:12-13, 15-16]
1
π/2
π
None
∫01dx2x−x2=∫01dx1−(x−1)2dx=[sin−1(x−1)]01=0−(−π2)=π2 \int_{0}^{1} \frac{\mathbf{d x}}{\sqrt{2 \mathrm{x}-\mathbf{x}^{2}}}=\int_{0}^{1} \frac{\mathrm{dx}}{\sqrt{1-(\mathrm{x}-1)^{2}}} \mathrm{dx}=\left[\sin ^{-1}(\mathrm{x}-1)\right]_{0}^{1}=0-\left(-\frac{\pi}{2}\right)=\frac{\pi}{2} ∫012x−x2dx=∫011−(x−1)2dxdx=[sin−1(x−1)]01=0−(−2π)=2π
∫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
